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Integral de (3x+1)/(x^4+2x^3+7x+8)*dx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 oo                       
  /                       
 |                        
 |        3*x + 1         
 |  ------------------- dx
 |   4      3             
 |  x  + 2*x  + 7*x + 8   
 |                        
/                         
1                         
$$\int\limits_{1}^{\infty} \frac{3 x + 1}{\left(7 x + \left(x^{4} + 2 x^{3}\right)\right) + 8}\, dx$$
Integral((3*x + 1)/(x^4 + 2*x^3 + 7*x + 8), (x, 1, oo))
Respuesta (Indefinida) [src]
                                                                                                                                                                                                         /                                                                                                                                             2\
                                                                                                                                                                                                         |                                                                                 /     ____________________                                 \ |
                                                                                                                                                                                                         |                                                                                 |    /              _____                                  | |
                                                                                                                                                                                                         |                                                                                 |   /   1     227*\/ 633                   4               | |
                                                                                                                                                                                                         |                                                                           15192*|3 /   ---- + -----------  - ------------------------------| |
                                                                                                                                                                                                         |                                                    ____________________         |\/    3798     21637206               ____________________| |
                                                                                                                                                                                                         |                                                   /              _____          |                                     /              _____ | |
                                                                                                                                         /     ____________________                                 \    |                                                  /   1     227*\/ 633           |                                    /   1     227*\/ 633  | |
                                                                                                                                         |    /              _____                                  |    |                                          5697*3 /   ---- + -----------          |                            5697*3 /   ---- + ----------- | |
                                                                                                                                         |   /   1     227*\/ 633                   4               |    | 97                     4                      \/    3798     21637206           \                                 \/    3798     21637206  / |
                                                                                                                                      25*|3 /   ---- + -----------  - ------------------------------|*log|--- + x - ----------------------------- + ------------------------------ + -------------------------------------------------------------------|
                                                                                                                                         |\/    3798     21637206               ____________________|    |227                ____________________                227                                                 227                                |
                                                        /                                          /                            2\\      |                                     /              _____ |    |                  /              _____                                                                                                        |
  /                                                     |      3         2                         |9272       58869*t   87354*t ||      |                                    /   1     227*\/ 633  |    |                 /   1     227*\/ 633                                                                                                         |
 |                                             2*RootSum|1899*t  - 1899*t  + 607*t - 64, t -> t*log|---- + x - ------- + --------||      |                            5697*3 /   ---- + ----------- |    |          227*3 /   ---- + -----------                                                                                                        |
 |       3*x + 1                2*log(1 + x)            \                                          \457          457       457   //      \                                 \/    3798     21637206  /    \              \/    3798     21637206                                                                                                         /
 | ------------------- dx = C - ------------ + ------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |  4      3                         9                                                  9                                                                                                                                                      9                                                                                                         
 | x  + 2*x  + 7*x + 8                                                                                                                                                                                                                                                                                                                                   
 |                                                                                                                                                                                                                                                                                                                                                       
/                                                                                                                                                                                                                                                                                                                                                        
$$\int \frac{3 x + 1}{\left(7 x + \left(x^{4} + 2 x^{3}\right)\right) + 8}\, dx = C - \frac{2 \log{\left(x + 1 \right)}}{9} + \frac{25 \left(- \frac{4}{5697 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}} + \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}\right) \log{\left(x - \frac{4}{227 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}} + \frac{15192 \left(- \frac{4}{5697 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}} + \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}\right)^{2}}{227} + \frac{97}{227} + \frac{5697 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}}{227} \right)}}{9} + \frac{2 \operatorname{RootSum} {\left(1899 t^{3} - 1899 t^{2} + 607 t - 64, \left( t \mapsto t \log{\left(\frac{87354 t^{2}}{457} - \frac{58869 t}{457} + x + \frac{9272}{457} \right)} \right)\right)}}{9}$$
Respuesta [src]
 oo                       
  /                       
 |                        
 |        1 + 3*x         
 |  ------------------- dx
 |       4      3         
 |  8 + x  + 2*x  + 7*x   
 |                        
/                         
1                         
$$\int\limits_{1}^{\infty} \frac{3 x + 1}{x^{4} + 2 x^{3} + 7 x + 8}\, dx$$
=
=
 oo                       
  /                       
 |                        
 |        1 + 3*x         
 |  ------------------- dx
 |       4      3         
 |  8 + x  + 2*x  + 7*x   
 |                        
/                         
1                         
$$\int\limits_{1}^{\infty} \frac{3 x + 1}{x^{4} + 2 x^{3} + 7 x + 8}\, dx$$
Integral((1 + 3*x)/(8 + x^4 + 2*x^3 + 7*x), (x, 1, oo))

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