Sr Examen
Integral de (3*x+1)/(x^4+2*x^3+7*x+8) dx
Solución
Ha introducido
[src]
oo / | | 3*x + 1 | ------------------- dx | 4 3 | x + 2*x + 7*x + 8 | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{3 x + 1}{\left(7 x + \left(x^{4} + 2 x^{3}\right)\right) + 8}\, dx$$
Integral((3*x + 1)/(x^4 + 2*x^3 + 7*x + 8), (x, -oo, 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
|
/
$$\int \frac{3 x + 1}{\left(7 x + \left(x^{4} + 2 x^{3}\right)\right) + 8}\, dx = C - \frac{2 \log{\left(x + 1 \right)}}{9} + \frac{25 \left(- \frac{4}{5697 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}} + \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}\right) \log{\left(x - \frac{4}{227 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}} + \frac{15192 \left(- \frac{4}{5697 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}} + \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}\right)^{2}}{227} + \frac{97}{227} + \frac{5697 \sqrt[3]{\frac{1}{3798} + \frac{227 \sqrt{633}}{21637206}}}{227} \right)}}{9} + \frac{2 \operatorname{RootSum} {\left(1899 t^{3} - 1899 t^{2} + 607 t - 64, \left( t \mapsto t \log{\left(\frac{87354 t^{2}}{457} - \frac{58869 t}{457} + x + \frac{9272}{457} \right)} \right)\right)}}{9}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.