Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
Integral de d{x}:
Integral de 1/(y+y^3)
Integral de 1/4x+3
Integral de (1-2*x)*exp(-2*x)
Integral de (1-2*x)/x^2
Expresiones idénticas
(x+ tres)/(4x^ tres +5x^ dos + tres)
(x más 3) dividir por (4x al cubo más 5x al cuadrado más 3)
(x más tres) dividir por (4x en el grado tres más 5x en el grado dos más tres)
(x+3)/(4x3+5x2+3)
x+3/4x3+5x2+3
(x+3)/(4x³+5x²+3)
(x+3)/(4x en el grado 3+5x en el grado 2+3)
x+3/4x^3+5x^2+3
(x+3) dividir por (4x^3+5x^2+3)
(x+3)/(4x^3+5x^2+3)dx
Expresiones semejantes
(x+3)/(4x^3+5x^2-3)
(x-3)/(4x^3+5x^2+3)
(x+3)/(4x^3-5x^2+3)

Resolución de integrales/ (x+3)/ x^3+5/ x^2+3/ (x+3)/(4x^3+5x^2+3)

Integral de (x+3)/(4x^3+5x^2+3) dx

Solución

Ha introducido [src]

 oo                   
  /                   
 |                    
 |       x + 3        
 |  --------------- dx
 |     3      2       
 |  4*x  + 5*x  + 3   
 |                    
/                     
0

$$\int\limits_{0}^{\infty} \frac{x + 3}{\left(4 x^{3} + 5 x^{2}\right) + 3}\, dx$$

Integral((x + 3)/(4*x^3 + 5*x^2 + 3), (x, 0, oo))

Solución detallada

Vuelva a escribir el integrando:

$\frac{x + 3}{\left(4 x^{3} + 5 x^{2}\right) + 3} = \frac{x}{\left(4 x^{3} + 5 x^{2}\right) + 3} + \frac{3}{\left(4 x^{3} + 5 x^{2}\right) + 3}$
Integramos término a término:
1. No puedo encontrar los pasos en la búsqueda de esta integral.
  
  Pero la integral
  
  $\operatorname{RootSum} {\left(1796 t^{3} - 15 t + 1, \left( t \mapsto t \log{\left(\frac{449 t^{2}}{3} + x - \frac{5}{12} \right)} \right)\right)}$
1. La integral del producto de una función por una constante es la constante por la integral de esta función:
  
  $\int \frac{3}{\left(4 x^{3} + 5 x^{2}\right) + 3}\, dx = 3 \int \frac{1}{\left(4 x^{3} + 5 x^{2}\right) + 3}\, dx$
  1. No puedo encontrar los pasos en la búsqueda de esta integral.
    
    Pero la integral
    
    $\left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right) \log{\left(x - \frac{25}{1546 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \frac{33675 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right)^{2}}{773} + \frac{1705}{3092} + \frac{8082 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}}{773} \right)}$
  Por lo tanto, el resultado es: $3 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right) \log{\left(x - \frac{25}{1546 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \frac{33675 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right)^{2}}{773} + \frac{1705}{3092} + \frac{8082 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}}{773} \right)}$
El resultado es: $3 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right) \log{\left(x - \frac{25}{1546 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \frac{33675 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right)^{2}}{773} + \frac{1705}{3092} + \frac{8082 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}}{773} \right)} + \operatorname{RootSum} {\left(1796 t^{3} - 15 t + 1, \left( t \mapsto t \log{\left(\frac{449 t^{2}}{3} + x - \frac{5}{12} \right)} \right)\right)}$
Ahora simplificar:

$\frac{\sqrt[3]{16164 + 773 \sqrt{449}} \left(\left(- \frac{15}{1796 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{15}{1796 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3}\right)^{2}}{3} \right)} + \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right)^{2}}{3} \right)} + \left(- \frac{\sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{\sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right)^{2}}{3} \right)}\right) - \frac{\sqrt[3]{449} \left(- \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}} + 25 \sqrt[3]{449}\right) \log{\left(x - \frac{3 \sqrt[6]{449} \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}}}{625} + \frac{5}{12} + \frac{449^{\frac{5}{6}} \sqrt[3]{16164 + 773 \sqrt{449}}}{5388} + \frac{773 \cdot 449^{\frac{2}{3}} \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}}}{3367500} \right)}}{898}}{\sqrt[3]{16164 + 773 \sqrt{449}}}$
Añadimos la constante de integración:

$\frac{\sqrt[3]{16164 + 773 \sqrt{449}} \left(\left(- \frac{15}{1796 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{15}{1796 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3}\right)^{2}}{3} \right)} + \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right)^{2}}{3} \right)} + \left(- \frac{\sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{\sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right)^{2}}{3} \right)}\right) - \frac{\sqrt[3]{449} \left(- \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}} + 25 \sqrt[3]{449}\right) \log{\left(x - \frac{3 \sqrt[6]{449} \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}}}{625} + \frac{5}{12} + \frac{449^{\frac{5}{6}} \sqrt[3]{16164 + 773 \sqrt{449}}}{5388} + \frac{773 \cdot 449^{\frac{2}{3}} \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}}}{3367500} \right)}}{898}}{\sqrt[3]{16164 + 773 \sqrt{449}}}+ \mathrm{constant}$

Respuesta:

$\frac{\sqrt[3]{16164 + 773 \sqrt{449}} \left(\left(- \frac{15}{1796 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{15}{1796 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3}\right)^{2}}{3} \right)} + \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right)^{2}}{3} \right)} + \left(- \frac{\sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right) \log{\left(x - \frac{5}{12} + \frac{449 \left(- \frac{\sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}{3} - \frac{15}{1796 \sqrt[3]{\frac{243 \sqrt{449}}{806404} + \frac{27}{3592}}}\right)^{2}}{3} \right)}\right) - \frac{\sqrt[3]{449} \left(- \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}} + 25 \sqrt[3]{449}\right) \log{\left(x - \frac{3 \sqrt[6]{449} \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}}}{625} + \frac{5}{12} + \frac{449^{\frac{5}{6}} \sqrt[3]{16164 + 773 \sqrt{449}}}{5388} + \frac{773 \cdot 449^{\frac{2}{3}} \left(16164 + 773 \sqrt{449}\right)^{\frac{2}{3}}}{3367500} \right)}}{898}}{\sqrt[3]{16164 + 773 \sqrt{449}}}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

                                                                                               /                                                                                                                                                2\                                                             
                                                                                               |                                                                                   /     ____________________                                  \ |                                                             
                                                                                               |                                                                                   |    /              _____                                   | |                                                             
                                                                                               |                                                                                   |   /   1     773*\/ 449                    25              | |                                                             
                                                                                               |                                                                             33675*|3 /   ---- + -----------  - -------------------------------| |                                                             
                                                                                               |                                                      ____________________         |\/    2694     43545816                ____________________| |                                                             
                                                                                               |                                                     /              _____          |                                      /              _____ | |                                                             
  /                           /     ____________________                                  \    |                                                    /   1     773*\/ 449           |                                     /   1     773*\/ 449  | |                                                             
 |                            |    /              _____                                   |    |                                            8082*3 /   ---- + -----------          |                            16164*3 /   ---- + ----------- | |          /                              /                2\\
 |      x + 3                 |   /   1     773*\/ 449                    25              |    |1705                     25                      \/    2694     43545816           \                                  \/    2694     43545816  / |          |      3                       |  5        449*t ||
 | --------------- dx = C + 3*|3 /   ---- + -----------  - -------------------------------|*log|---- + x - ------------------------------ + ------------------------------ + --------------------------------------------------------------------| + RootSum|1796*t  - 15*t + 1, t -> t*log|- -- + x + ------||
 |    3      2                |\/    2694     43545816                ____________________|    |3092                 ____________________                773                                                 773                                 |          \                              \  12         3   //
 | 4*x  + 5*x  + 3            |                                      /              _____ |    |                    /              _____                                                                                                         |                                                             
 |                            |                                     /   1     773*\/ 449  |    |                   /   1     773*\/ 449                                                                                                          |                                                             
/                             |                            16164*3 /   ---- + ----------- |    |           1546*3 /   ---- + -----------                                                                                                         |                                                             
                              \                                  \/    2694     43545816  /    \                \/    2694     43545816                                                                                                          /

$$\int \frac{x + 3}{\left(4 x^{3} + 5 x^{2}\right) + 3}\, dx = C + 3 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right) \log{\left(x - \frac{25}{1546 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \frac{33675 \left(- \frac{25}{16164 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}} + \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}\right)^{2}}{773} + \frac{1705}{3092} + \frac{8082 \sqrt[3]{\frac{1}{2694} + \frac{773 \sqrt{449}}{43545816}}}{773} \right)} + \operatorname{RootSum} {\left(1796 t^{3} - 15 t + 1, \left( t \mapsto t \log{\left(\frac{449 t^{2}}{3} + x - \frac{5}{12} \right)} \right)\right)}$$

Simplificar

Gráfica

Trazar el gráfico f(x)

Respuesta [src]

oo

$$\infty$$

oo

$$\infty$$

oo

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

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Integral de (x+3)/(4x^3+5x^2+3) dx

Límites de integración:

Gráfico:

Definida a trozos:

Solución