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Expresiones idénticas
(tres x²+1dx)/(3√(dos x³+2x+2)²)
(3x² más 1dx) dividir por (3√(2x³ más 2x más 2)²)
(tres x² más 1dx) dividir por (3√(dos x³ más 2x más 2)²)
3x²+1dx/3√2x³+2x+2²
(3x²+1dx) dividir por (3√(2x³+2x+2)²)
Expresiones semejantes
(3x²+1dx)/(3√(2x³-2x+2)²)
(3x²-1dx)/(3√(2x³+2x+2)²)
(3x²+1dx)/(3√(2x³+2x-2)²)
(3x²+1dx)/(3(√(2x³+2x+2)²))

Resolución de integrales/ 3x²+1/ (3x²+1dx)/(3√(2x³+2x+2)²)

Integral de (3x²+1dx)/(3√(2x³+2x+2)²) dx

Solución

Ha introducido [src]

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

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

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

Solución detallada

Vuelva a escribir el integrando:

$\frac{3 x^{2} + 1}{3 \left(\sqrt{\left(2 x^{3} + 2 x\right) + 2}\right)^{2}} = \frac{x^{2}}{\left(2 x^{3} + 2 x\right) + 2} + \frac{1}{3 \left(\left(2 x^{3} + 2 x\right) + 2\right)}$
Integramos término a término:
1. Vuelva a escribir el integrando:
  
  $\frac{x^{2}}{\left(2 x^{3} + 2 x\right) + 2} = \frac{x^{2}}{2 \left(x^{3} + x + 1\right)}$
2. La integral del producto de una función por una constante es la constante por la integral de esta función:
  
  $\int \frac{x^{2}}{2 \left(x^{3} + x + 1\right)}\, dx = \frac{\int \frac{x^{2}}{x^{3} + x + 1}\, dx}{2}$
  1. No puedo encontrar los pasos en la búsqueda de esta integral.
    
    Pero la integral
    
    $\operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 10 t - 1, \left( t \mapsto t \log{\left(- 62 t^{2} + 31 t + x - 3 \right)} \right)\right)}$
  Por lo tanto, el resultado es: $\frac{\operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 10 t - 1, \left( t \mapsto t \log{\left(- 62 t^{2} + 31 t + x - 3 \right)} \right)\right)}}{2}$
1. La integral del producto de una función por una constante es la constante por la integral de esta función:
  
  $\int \frac{1}{3 \left(\left(2 x^{3} + 2 x\right) + 2\right)}\, dx = \frac{\int \frac{1}{\left(2 x^{3} + 2 x\right) + 2}\, dx}{3}$
  1. Vuelva a escribir el integrando:
    
    $\frac{1}{\left(2 x^{3} + 2 x\right) + 2} = \frac{1}{2 \left(x^{3} + x + 1\right)}$
  2. La integral del producto de una función por una constante es la constante por la integral de esta función:
    
    $\int \frac{1}{2 \left(x^{3} + x + 1\right)}\, dx = \frac{\int \frac{1}{x^{3} + x + 1}\, dx}{2}$
    1. No puedo encontrar los pasos en la búsqueda de esta integral.
      
      Pero la integral
      
      $\operatorname{RootSum} {\left(31 t^{3} - 3 t - 1, \left( t \mapsto t \log{\left(- \frac{62 t^{2}}{9} + \frac{31 t}{9} + x + \frac{4}{9} \right)} \right)\right)}$
    Por lo tanto, el resultado es: $\frac{\operatorname{RootSum} {\left(31 t^{3} - 3 t - 1, \left( t \mapsto t \log{\left(- \frac{62 t^{2}}{9} + \frac{31 t}{9} + x + \frac{4}{9} \right)} \right)\right)}}{2}$
  Por lo tanto, el resultado es: $\frac{\operatorname{RootSum} {\left(31 t^{3} - 3 t - 1, \left( t \mapsto t \log{\left(- \frac{62 t^{2}}{9} + \frac{31 t}{9} + x + \frac{4}{9} \right)} \right)\right)}}{6}$
El resultado es: $\frac{\operatorname{RootSum} {\left(31 t^{3} - 3 t - 1, \left( t \mapsto t \log{\left(- \frac{62 t^{2}}{9} + \frac{31 t}{9} + x + \frac{4}{9} \right)} \right)\right)}}{6} + \frac{\operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 10 t - 1, \left( t \mapsto t \log{\left(- 62 t^{2} + 31 t + x - 3 \right)} \right)\right)}}{2}$
Ahora simplificar:

$\frac{\left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}} + \frac{1}{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right) \log{\left(x + \frac{4}{9} + \frac{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} - \frac{62 \left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}} + \frac{1}{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right)^{2}}{9} + \frac{1}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} \right)}}{6} + \frac{\left(\frac{1}{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right) \log{\left(x + \frac{4}{9} + \frac{1}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{62 \left(\frac{1}{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right)^{2}}{9} + \frac{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} \right)}}{6} + \frac{\left(\frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right) \log{\left(x + \frac{22}{3} - \frac{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - 62 \left(\frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right)^{2} \right)}}{2} + \frac{\left(\frac{1}{3} - \frac{1}{93 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3}\right) \log{\left(x + \frac{22}{3} - 62 \left(\frac{1}{3} - \frac{1}{93 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3}\right)^{2} - \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} \right)}}{2} + \frac{\left(- \frac{\sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{1}{3}\right) \log{\left(x - \frac{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - 62 \left(- \frac{\sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{1}{3}\right)^{2} - \frac{1}{3 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{22}{3} \right)}}{2} + \frac{\left(\frac{1}{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right) \log{\left(x - \frac{62 \left(\frac{1}{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right)^{2}}{9} + \frac{1}{9 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{4}{9} + \frac{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} \right)}}{6}$
Añadimos la constante de integración:

$\frac{\left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}} + \frac{1}{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right) \log{\left(x + \frac{4}{9} + \frac{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} - \frac{62 \left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}} + \frac{1}{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right)^{2}}{9} + \frac{1}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} \right)}}{6} + \frac{\left(\frac{1}{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right) \log{\left(x + \frac{4}{9} + \frac{1}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{62 \left(\frac{1}{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right)^{2}}{9} + \frac{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} \right)}}{6} + \frac{\left(\frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right) \log{\left(x + \frac{22}{3} - \frac{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - 62 \left(\frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right)^{2} \right)}}{2} + \frac{\left(\frac{1}{3} - \frac{1}{93 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3}\right) \log{\left(x + \frac{22}{3} - 62 \left(\frac{1}{3} - \frac{1}{93 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3}\right)^{2} - \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} \right)}}{2} + \frac{\left(- \frac{\sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{1}{3}\right) \log{\left(x - \frac{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - 62 \left(- \frac{\sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{1}{3}\right)^{2} - \frac{1}{3 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{22}{3} \right)}}{2} + \frac{\left(\frac{1}{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right) \log{\left(x - \frac{62 \left(\frac{1}{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right)^{2}}{9} + \frac{1}{9 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{4}{9} + \frac{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} \right)}}{6}+ \mathrm{constant}$

Respuesta:

$\frac{\left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}} + \frac{1}{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right) \log{\left(x + \frac{4}{9} + \frac{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} - \frac{62 \left(\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}} + \frac{1}{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right)^{2}}{9} + \frac{1}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} \right)}}{6} + \frac{\left(\frac{1}{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right) \log{\left(x + \frac{4}{9} + \frac{1}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{62 \left(\frac{1}{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right)^{2}}{9} + \frac{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} \right)}}{6} + \frac{\left(\frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right) \log{\left(x + \frac{22}{3} - \frac{31 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - 62 \left(\frac{1}{3} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}\right)^{2} \right)}}{2} + \frac{\left(\frac{1}{3} - \frac{1}{93 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3}\right) \log{\left(x + \frac{22}{3} - 62 \left(\frac{1}{3} - \frac{1}{93 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3}\right)^{2} - \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} - \frac{31 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} \right)}}{2} + \frac{\left(- \frac{\sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{1}{3}\right) \log{\left(x - \frac{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - 62 \left(- \frac{\sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{3} - \frac{1}{93 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{1}{3}\right)^{2} - \frac{1}{3 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{22}{3} \right)}}{2} + \frac{\left(\frac{1}{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right) \log{\left(x - \frac{62 \left(\frac{1}{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}\right)^{2}}{9} + \frac{1}{9 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}} + \frac{4}{9} + \frac{31 \sqrt[3]{\frac{3 \sqrt{93}}{1922} + \frac{1}{62}}}{9} \right)}}{6}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

  /                                                                                                              /                           /            2       \\
 |                                                                                                               |    3                      |4       62*t    31*t||
 |           2                            /    3       2                       /             2       \\   RootSum|31*t  - 3*t - 1, t -> t*log|- + x - ----- + ----||
 |        3*x  + 1                 RootSum\31*t  - 31*t  + 10*t - 1, t -> t*log\-3 + x - 62*t  + 31*t//          \                           \9         9      9  //
 | ---------------------- dx = C + -------------------------------------------------------------------- + ----------------------------------------------------------
 |                      2                                           2                                                                 6                             
 |      ________________                                                                                                                                            
 |     /    3                                                                                                                                                       
 | 3*\/  2*x  + 2*x + 2                                                                                                                                             
 |                                                                                                                                                                  
/

$$\int \frac{3 x^{2} + 1}{3 \left(\sqrt{\left(2 x^{3} + 2 x\right) + 2}\right)^{2}}\, dx = C + \frac{\operatorname{RootSum} {\left(31 t^{3} - 3 t - 1, \left( t \mapsto t \log{\left(- \frac{62 t^{2}}{9} + \frac{31 t}{9} + x + \frac{4}{9} \right)} \right)\right)}}{6} + \frac{\operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 10 t - 1, \left( t \mapsto t \log{\left(- 62 t^{2} + 31 t + x - 3 \right)} \right)\right)}}{2}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

log(3)
------
  6

$$\frac{\log{\left(3 \right)}}{6}$$

log(3)
------
  6

$$\frac{\log{\left(3 \right)}}{6}$$

log(3)/6

Respuesta numérica [src]

0.183102048111352

0.183102048111352

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Integral de (3x²+1dx)/(3√(2x³+2x+2)²) dx

Límites de integración:

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Definida a trozos:

Solución