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Expresiones semejantes
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Resolución de integrales/ x^2*x/ (x+1)/ 20*x^2/ 20*x^2/(((x^2*x-3)*(x+1)))

Integral de 20x^2/(((x^2x-3)*(x+1))) dx

Solución

Ha introducido [src]

  1                      
  /                      
 |                       
 |            2          
 |        20*x           
 |  ------------------ dx
 |  / 2      \           
 |  \x *x - 3/*(x + 1)   
 |                       
/                        
0

$$\int\limits_{0}^{1} \frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)}\, dx$$

Integral((20*x^2)/(((x^2*x - 3)*(x + 1))), (x, 0, 1))

Solución detallada

Hay varias maneras de calcular esta integral.
Método #1
1. Vuelva a escribir el integrando:
  
  $\frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)} = \frac{5 \left(x^{2} + 3 x - 3\right)}{x^{3} - 3} - \frac{5}{x + 1}$
2. Integramos término a término:
  1. La integral del producto de una función por una constante es la constante por la integral de esta función:
    
    $\int \frac{5 \left(x^{2} + 3 x - 3\right)}{x^{3} - 3}\, dx = 5 \int \frac{x^{2} + 3 x - 3}{x^{3} - 3}\, dx$
    1. Vuelva a escribir el integrando:
      
      $\frac{x^{2} + 3 x - 3}{x^{3} - 3} = \frac{x^{2}}{x^{3} - 3} + \frac{3 x}{x^{3} - 3} - \frac{3}{x^{3} - 3}$
    2. Integramos término a término:
      
      que $u = x^{3} - 3$ .
      
      Luego que $du = 3 x^{2} dx$ y ponemos $\frac{du}{3}$ :
      
      $\int \frac{1}{3 u}\, du$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
      
      Integral $\frac{1}{u}$ es $\log{\left(u \right)}$ .
      
      Por lo tanto, el resultado es: $\frac{\log{\left(u \right)}}{3}$
      
      Si ahora sustituir $u$ más en:
      
      $\frac{\log{\left(x^{3} - 3 \right)}}{3}$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{3 x}{x^{3} - 3}\, dx = 3 \int \frac{x}{x^{3} - 3}\, dx$
      
      No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$
      
      Por lo tanto, el resultado es: $\frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \left(- \frac{3}{x^{3} - 3}\right)\, dx = - 3 \int \frac{1}{x^{3} - 3}\, dx$
      
      No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}$
      
      Por lo tanto, el resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$
      
      El resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\log{\left(x^{3} - 3 \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
    Por lo tanto, el resultado es: $- \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
  1. La integral del producto de una función por una constante es la constante por la integral de esta función:
    
    $\int \left(- \frac{5}{x + 1}\right)\, dx = - 5 \int \frac{1}{x + 1}\, dx$
    1. que $u = x + 1$ .
      
      Luego que $du = dx$ y ponemos $du$ :
      
      $\int \frac{1}{u}\, du$
      
      Integral $\frac{1}{u}$ es $\log{\left(u \right)}$ .
      
      Si ahora sustituir $u$ más en:
      
      $\log{\left(x + 1 \right)}$
    Por lo tanto, el resultado es: $- 5 \log{\left(x + 1 \right)}$
  El resultado es: $- 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
Método #2
1. Vuelva a escribir el integrando:
  
  $\frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)} = \frac{20 x^{2}}{x^{4} + x^{3} - 3 x - 3}$
2. La integral del producto de una función por una constante es la constante por la integral de esta función:
  
  $\int \frac{20 x^{2}}{x^{4} + x^{3} - 3 x - 3}\, dx = 20 \int \frac{x^{2}}{x^{4} + x^{3} - 3 x - 3}\, dx$
  1. Vuelva a escribir el integrando:
    
    $\frac{x^{2}}{x^{4} + x^{3} - 3 x - 3} = \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)} - \frac{1}{4 \left(x + 1\right)}$
  2. Integramos término a término:
    1. La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)}\, dx = \frac{\int \frac{x^{2} + 3 x - 3}{x^{3} - 3}\, dx}{4}$
      
      Vuelva a escribir el integrando:
      
      $\frac{x^{2} + 3 x - 3}{x^{3} - 3} = \frac{x^{2}}{x^{3} - 3} + \frac{3 x}{x^{3} - 3} - \frac{3}{x^{3} - 3}$
      
      Integramos término a término:
      
      que $u = x^{3} - 3$ .
      
      Luego que $du = 3 x^{2} dx$ y ponemos $\frac{du}{3}$ :
      
      $\int \frac{1}{3 u}\, du$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
      
      Integral $\frac{1}{u}$ es $\log{\left(u \right)}$ .
      
      Por lo tanto, el resultado es: $\frac{\log{\left(u \right)}}{3}$
      
      Si ahora sustituir $u$ más en:
      
      $\frac{\log{\left(x^{3} - 3 \right)}}{3}$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{3 x}{x^{3} - 3}\, dx = 3 \int \frac{x}{x^{3} - 3}\, dx$
      
      No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$
      
      Por lo tanto, el resultado es: $\frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \left(- \frac{3}{x^{3} - 3}\right)\, dx = - 3 \int \frac{1}{x^{3} - 3}\, dx$
      
      No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}$
      
      Por lo tanto, el resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$
      
      El resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\log{\left(x^{3} - 3 \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
      
      Por lo tanto, el resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4}$
    1. La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \left(- \frac{1}{4 \left(x + 1\right)}\right)\, dx = - \frac{\int \frac{1}{x + 1}\, dx}{4}$
      
      que $u = x + 1$ .
      
      Luego que $du = dx$ y ponemos $du$ :
      
      $\int \frac{1}{u}\, du$
      
      Integral $\frac{1}{u}$ es $\log{\left(u \right)}$ .
      
      Si ahora sustituir $u$ más en:
      
      $\log{\left(x + 1 \right)}$
      
      Por lo tanto, el resultado es: $- \frac{\log{\left(x + 1 \right)}}{4}$
    El resultado es: $- \frac{\log{\left(x + 1 \right)}}{4} - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4}$
  Por lo tanto, el resultado es: $- 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
Método #3
1. Vuelva a escribir el integrando:
  
  $\frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)} = \frac{20 x^{2}}{x^{4} - 3 x + x x^{2} - 3}$
2. La integral del producto de una función por una constante es la constante por la integral de esta función:
  
  $\int \frac{20 x^{2}}{x^{4} - 3 x + x x^{2} - 3}\, dx = 20 \int \frac{x^{2}}{x^{4} - 3 x + x x^{2} - 3}\, dx$
  1. Vuelva a escribir el integrando:
    
    $\frac{x^{2}}{x^{4} - 3 x + x x^{2} - 3} = \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)} - \frac{1}{4 \left(x + 1\right)}$
  2. Integramos término a término:
    1. La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)}\, dx = \frac{\int \frac{x^{2} + 3 x - 3}{x^{3} - 3}\, dx}{4}$
      
      Vuelva a escribir el integrando:
      
      $\frac{x^{2} + 3 x - 3}{x^{3} - 3} = \frac{x^{2}}{x^{3} - 3} + \frac{3 x}{x^{3} - 3} - \frac{3}{x^{3} - 3}$
      
      Integramos término a término:
      
      que $u = x^{3} - 3$ .
      
      Luego que $du = 3 x^{2} dx$ y ponemos $\frac{du}{3}$ :
      
      $\int \frac{1}{3 u}\, du$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3}$
      
      Integral $\frac{1}{u}$ es $\log{\left(u \right)}$ .
      
      Por lo tanto, el resultado es: $\frac{\log{\left(u \right)}}{3}$
      
      Si ahora sustituir $u$ más en:
      
      $\frac{\log{\left(x^{3} - 3 \right)}}{3}$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \frac{3 x}{x^{3} - 3}\, dx = 3 \int \frac{x}{x^{3} - 3}\, dx$
      
      No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$
      
      Por lo tanto, el resultado es: $\frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
      
      La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \left(- \frac{3}{x^{3} - 3}\right)\, dx = - 3 \int \frac{1}{x^{3} - 3}\, dx$
      
      No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}$
      
      Por lo tanto, el resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$
      
      El resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\log{\left(x^{3} - 3 \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
      
      Por lo tanto, el resultado es: $- \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4}$
    1. La integral del producto de una función por una constante es la constante por la integral de esta función:
      
      $\int \left(- \frac{1}{4 \left(x + 1\right)}\right)\, dx = - \frac{\int \frac{1}{x + 1}\, dx}{4}$
      
      que $u = x + 1$ .
      
      Luego que $du = dx$ y ponemos $du$ :
      
      $\int \frac{1}{u}\, du$
      
      Integral $\frac{1}{u}$ es $\log{\left(u \right)}$ .
      
      Si ahora sustituir $u$ más en:
      
      $\log{\left(x + 1 \right)}$
      
      Por lo tanto, el resultado es: $- \frac{\log{\left(x + 1 \right)}}{4}$
    El resultado es: $- \frac{\log{\left(x + 1 \right)}}{4} - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4}$
  Por lo tanto, el resultado es: $- 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$
Añadimos la constante de integración:

$- 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}+ \mathrm{constant}$

Respuesta:

$- 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

  /                                                                                                                                                                                            /  ___       6 ___\                                   
 |                                                                                                                                                                                     5/6     |\/ 3    2*x*\/ 3 |                                   
 |           2                                     /      3\               /  ___       6 ___\     3 ___    /    3 ___\      2/3    / 2/3    2     3 ___\      2/3    /    3 ___\   5*3   *atan|----- + ---------|     3 ___    / 2/3    2     3 ___\
 |       20*x                                 5*log\-3 + x /     6 ___     |\/ 3    2*x*\/ 3 |   5*\/ 3 *log\x - \/ 3 /   5*3   *log\3    + x  + x*\/ 3 /   5*3   *log\x - \/ 3 /              \  3         3    /   5*\/ 3 *log\3    + x  + x*\/ 3 /
 | ------------------ dx = C - 5*log(1 + x) + -------------- + 5*\/ 3 *atan|----- + ---------| - ---------------------- - ------------------------------- + --------------------- + ------------------------------ + --------------------------------
 | / 2      \                                       3                      \  3         3    /             3                             6                            3                           3                                 6                
 | \x *x - 3/*(x + 1)                                                                                                                                                                                                                                
 |                                                                                                                                                                                                                                                   
/

$$\int \frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)}\, dx = C - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

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                     __________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |          |                               /     3 ___    2/3\         /     3 ___    2/3\ ||                                                                                                                                                                                           |          |                                 /     3 ___    2/3\         /     3 ___    2/3\ ||                                                                                                                                                                                                 __________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                    /    _______________                            /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             _______________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   _______________                                                                                                                                                                                                                                                  _______________                                                                                                                \      |          |                               |1    \/ 3    3   |         |1    \/ 3    3   | ||                                                 /                                   _______________                                _______________                  _______________\      |          |                                 |1    \/ 3    3   |         |1    \/ 3    3   | ||                                                 /                                   _______________                                _______________                  _______________\           /    _______________                            /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             _______________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   _______________                                                                                                                                                                                                                                                  _______________                                                                                                                \
                   /    /           2/3    3 ___ /      3 ___\      |                                                                                                                                                                                                                                                                                                                                                                                                 2/3                                                                                                                                                                                                                                                        /           2/3                                                                                                                                                                                                                                                      3 ___                                                                                                                                                                                                                                                  2/3   /           2/3                                                                                                                                                                                                                                          3 ___   /           2/3                                                                                                                 |      |          |         3 ___       2/3   288*|-- - ----- + ----|    6480*|-- - ----- + ----| || /     3 ___    2/3\      /      2/3   3 ___\    |                 3 ___            /           2/3            2/3         3 ___   /           2/3            2/3   /           2/3 |      |          |           3 ___       2/3   288*|-- - ----- + ----|    6480*|-- - ----- + ----| || /     3 ___    2/3\      /      2/3   3 ___\    |                 3 ___            /           2/3            2/3         3 ___   /           2/3            2/3   /           2/3 |          /    /           2/3    3 ___ /      3 ___\      |                                                                                                                                                                                                                                                                                                                                                                                                 2/3                                                                                                                                                                                                                                                        /           2/3                                                                                                                                                                                                                                                      3 ___                                                                                                                                                                                                                                                  2/3   /           2/3                                                                                                                                                                                                                                          3 ___   /           2/3                                                                                                                 |
                  /   \/  -15 + 16*3       \/ 3 *\7 - 3*\/ 3 /      |                                                                                                                               1726                                                                                                                                                                                                                                                          39*3                                                                                                                                                                                                                                                     318*\/  -15 + 16*3                                                                                                                                                                                                                                                    1465*\/ 3                                                                                                                                                                                                                                              135*3   *\/  -15 + 16*3                                                                                                                                                                                                                                         135*\/ 3 *\/  -15 + 16*3                                                                                                                    |      |          |205   21*\/ 3    21*3          \12     12     12 /         \12     12     12 / || |1    \/ 3    3   |      |1    3      \/ 3 |    |975663   1732071*\/ 3    178059*\/  -15 + 16*3       345431*3      15207*\/ 3 *\/  -15 + 16*3       162369*3   *\/  -15 + 16*3    |      |          |   7    21*\/ 3    21*3          \12     12     12 /         \12     12     12 / || |1    \/ 3    3   |      |1    3      \/ 3 |    |747763   1421491*\/ 3    144351*\/  -15 + 16*3       353699*3      43827*\/ 3 *\/  -15 + 16*3       133749*3   *\/  -15 + 16*3    |         /   \/  -15 + 16*3       \/ 3 *\7 - 3*\/ 3 /      |                                                                                                                               2574                                                                                                                                                                                                                                                          39*3                                                                                                                                                                                                                                                     318*\/  -15 + 16*3                                                                                                                                                                                                                                                    1465*\/ 3                                                                                                                                                                                                                                              135*3   *\/  -15 + 16*3                                                                                                                                                                                                                                         135*\/ 3 *\/  -15 + 16*3                                                                                                                    |
-5*log(2) - 40*  /    ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - 20*|pi*I + log|--- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| - 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 20*|pi*I + log|- --- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| + 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 40*  /    ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
               \/             96                   192              |                 ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________|      \          \212     212        212                53                          53           // \12     12     12 /      \12    24      24 /    \44944        89888                 44944                89888                  89888                            89888             /      \          \  212     212        212                53                          53           // \12     12     12 /      \12    24      24 /    \44944        89888                 44944                89888                  89888                            89888             /      \/             96                   192              |                 ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________|
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                                                                    |       6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___ |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |       6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___ |
                                                                    \  - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \  - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3  /

$$40 \sqrt{\frac{\sqrt[3]{3} \left(7 - 3 \sqrt[3]{3}\right)}{192} + \frac{\sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{96}} \operatorname{atan}{\left(\frac{1465 \sqrt[3]{3}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{318 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{135 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{39 \cdot 3^{\frac{2}{3}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{135 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{2574}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} \right)} - 5 \log{\left(2 \right)} - 20 \left(- \frac{3^{\frac{2}{3}}}{24} + \frac{\sqrt[3]{3}}{24} + \frac{1}{12}\right) \log{\left(- \frac{1732071 \sqrt[3]{3}}{89888} - \frac{178059 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{44944} + \frac{15207 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{345431 \cdot 3^{\frac{2}{3}}}{89888} + \frac{162369 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{975663}{44944} \right)} + 20 \left(- \frac{3^{\frac{2}{3}}}{24} + \frac{\sqrt[3]{3}}{24} + \frac{1}{12}\right) \log{\left(- \frac{1421491 \sqrt[3]{3}}{89888} - \frac{144351 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{44944} + \frac{43827 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{353699 \cdot 3^{\frac{2}{3}}}{89888} + \frac{133749 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{747763}{44944} \right)} - 40 \sqrt{\frac{\sqrt[3]{3} \left(7 - 3 \sqrt[3]{3}\right)}{192} + \frac{\sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{96}} \operatorname{atan}{\left(\frac{1465 \sqrt[3]{3}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{318 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{135 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{39 \cdot 3^{\frac{2}{3}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{135 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{1726}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} \right)} - 20 \left(\log{\left(- \frac{21 \sqrt[3]{3}}{212} + \frac{288 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{2}}{53} + \frac{21 \cdot 3^{\frac{2}{3}}}{212} + \frac{6480 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{3}}{53} + \frac{205}{212} \right)} + i \pi\right) \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right) + 20 \left(\log{\left(- \frac{21 \sqrt[3]{3}}{212} - \frac{7}{212} + \frac{288 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{2}}{53} + \frac{21 \cdot 3^{\frac{2}{3}}}{212} + \frac{6480 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{3}}{53} \right)} + i \pi\right) \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)$$

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           /          /                                                  2                           3\\                                                                                                                                                                                           /          /                                                    2                           3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 
                     __________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |          |                               /     3 ___    2/3\         /     3 ___    2/3\ ||                                                                                                                                                                                           |          |                                 /     3 ___    2/3\         /     3 ___    2/3\ ||                                                                                                                                                                                                 __________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                    /    _______________                            /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             _______________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   _______________                                                                                                                                                                                                                                                  _______________                                                                                                                \      |          |                               |1    \/ 3    3   |         |1    \/ 3    3   | ||                                                 /                                   _______________                                _______________                  _______________\      |          |                                 |1    \/ 3    3   |         |1    \/ 3    3   | ||                                                 /                                   _______________                                _______________                  _______________\           /    _______________                            /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             _______________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   _______________                                                                                                                                                                                                                                                  _______________                                                                                                                \
                   /    /           2/3    3 ___ /      3 ___\      |                                                                                                                                                                                                                                                                                                                                                                                                 2/3                                                                                                                                                                                                                                                        /           2/3                                                                                                                                                                                                                                                      3 ___                                                                                                                                                                                                                                                  2/3   /           2/3                                                                                                                                                                                                                                          3 ___   /           2/3                                                                                                                 |      |          |         3 ___       2/3   288*|-- - ----- + ----|    6480*|-- - ----- + ----| || /     3 ___    2/3\      /      2/3   3 ___\    |                 3 ___            /           2/3            2/3         3 ___   /           2/3            2/3   /           2/3 |      |          |           3 ___       2/3   288*|-- - ----- + ----|    6480*|-- - ----- + ----| || /     3 ___    2/3\      /      2/3   3 ___\    |                 3 ___            /           2/3            2/3         3 ___   /           2/3            2/3   /           2/3 |          /    /           2/3    3 ___ /      3 ___\      |                                                                                                                                                                                                                                                                                                                                                                                                 2/3                                                                                                                                                                                                                                                        /           2/3                                                                                                                                                                                                                                                      3 ___                                                                                                                                                                                                                                                  2/3   /           2/3                                                                                                                                                                                                                                          3 ___   /           2/3                                                                                                                 |
                  /   \/  -15 + 16*3       \/ 3 *\7 - 3*\/ 3 /      |                                                                                                                               1726                                                                                                                                                                                                                                                          39*3                                                                                                                                                                                                                                                     318*\/  -15 + 16*3                                                                                                                                                                                                                                                    1465*\/ 3                                                                                                                                                                                                                                              135*3   *\/  -15 + 16*3                                                                                                                                                                                                                                         135*\/ 3 *\/  -15 + 16*3                                                                                                                    |      |          |205   21*\/ 3    21*3          \12     12     12 /         \12     12     12 / || |1    \/ 3    3   |      |1    3      \/ 3 |    |975663   1732071*\/ 3    178059*\/  -15 + 16*3       345431*3      15207*\/ 3 *\/  -15 + 16*3       162369*3   *\/  -15 + 16*3    |      |          |   7    21*\/ 3    21*3          \12     12     12 /         \12     12     12 / || |1    \/ 3    3   |      |1    3      \/ 3 |    |747763   1421491*\/ 3    144351*\/  -15 + 16*3       353699*3      43827*\/ 3 *\/  -15 + 16*3       133749*3   *\/  -15 + 16*3    |         /   \/  -15 + 16*3       \/ 3 *\7 - 3*\/ 3 /      |                                                                                                                               2574                                                                                                                                                                                                                                                          39*3                                                                                                                                                                                                                                                     318*\/  -15 + 16*3                                                                                                                                                                                                                                                    1465*\/ 3                                                                                                                                                                                                                                              135*3   *\/  -15 + 16*3                                                                                                                                                                                                                                         135*\/ 3 *\/  -15 + 16*3                                                                                                                    |
-5*log(2) - 40*  /    ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - 20*|pi*I + log|--- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| - 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 20*|pi*I + log|- --- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| + 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 40*  /    ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
               \/             96                   192              |                 ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________|      \          \212     212        212                53                          53           // \12     12     12 /      \12    24      24 /    \44944        89888                 44944                89888                  89888                            89888             /      \          \  212     212        212                53                          53           // \12     12     12 /      \12    24      24 /    \44944        89888                 44944                89888                  89888                            89888             /      \/             96                   192              |                 ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________                  ___________________________________________               ___________________________________________                ___________________________________________                                   ___________________________________________|
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                                                                    |       6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___ |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |       6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___         6 ___   /       2/3       /           2/3      3 ___        5/6   /       2/3       /           2/3      3 ___         ___   /       2/3       /           2/3      3 ___         ___   /           2/3    /       2/3       /           2/3      3 ___ |
                                                                    \  - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \  - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3     - 48*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 16*3   *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   + 29*\/ 3 *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3   - 45*\/ 3 *\/  -15 + 16*3    *\/   - 3*3    + 2*\/  -15 + 16*3     + 7*\/ 3  /

-5*log(2) - 40*sqrt(sqrt(-15 + 16*3^(2/3))/96 + 3^(1/3)*(7 - 3*3^(1/3))/192)*atan(-1726/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 39*3^(2/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 318*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 1465*3^(1/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) - 135*3^(2/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 135*3^(1/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)))) - 20*(pi*i + log(205/212 - 21*3^(1/3)/212 + 21*3^(2/3)/212 + 288*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^2/53 + 6480*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^3/53))*(1/12 - 3^(1/3)/12 + 3^(2/3)/12) - 20*(1/12 - 3^(2/3)/24 + 3^(1/3)/24)*log(975663/44944 - 1732071*3^(1/3)/89888 - 178059*sqrt(-15 + 16*3^(2/3))/44944 + 345431*3^(2/3)/89888 + 15207*3^(1/3)*sqrt(-15 + 16*3^(2/3))/89888 + 162369*3^(2/3)*sqrt(-15 + 16*3^(2/3))/89888) + 20*(pi*i + log(-7/212 - 21*3^(1/3)/212 + 21*3^(2/3)/212 + 288*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^2/53 + 6480*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^3/53))*(1/12 - 3^(1/3)/12 + 3^(2/3)/12) + 20*(1/12 - 3^(2/3)/24 + 3^(1/3)/24)*log(747763/44944 - 1421491*3^(1/3)/89888 - 144351*sqrt(-15 + 16*3^(2/3))/44944 + 353699*3^(2/3)/89888 + 43827*3^(1/3)*sqrt(-15 + 16*3^(2/3))/89888 + 133749*3^(2/3)*sqrt(-15 + 16*3^(2/3))/89888) + 40*sqrt(sqrt(-15 + 16*3^(2/3))/96 + 3^(1/3)*(7 - 3*3^(1/3))/192)*atan(-2574/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 39*3^(2/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 318*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 1465*3^(1/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) - 135*3^(2/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 135*3^(1/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))))

Respuesta numérica [src]

-1.54613462726938

-1.54613462726938

Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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Expresiones semejantes

Integral de 20x^2/(((x^2x-3)*(x+1))) dx

Límites de integración:

Gráfico:

Definida a trozos:

Solución

Método #1

Método #2

Método #3

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Integral de 20*x^2/(((x^2*x-3)*(x+1))) dx

Límites de integración:

Gráfico:

Definida a trozos:

Solución

Método #1

Método #2

Método #3

Integral de 20x^2/(((x^2x-3)*(x+1))) dx