Sr Examen
Integral de dx/(x*(x+3)^1/5) dx
Solución
Ha introducido
[src]
oo / | | 1 | ----------- dx | 5 _______ | x*\/ x + 3 | / 0
$$\int\limits_{0}^{\infty} \frac{1}{x \sqrt[5]{x + 3}}\, dx$$
Integral(1/(x*(x + 3)^(1/5)), (x, 0, oo))
Respuesta (Indefinida)
[src]
/ 4*pi*I\ / 8*pi*I\ / 6*pi*I\ / 2*pi*I\
-4*pi*I | ------| 2*pi*I | ------| 4*pi*I | ------| 3*pi*I | ------|
/ 5 ___ 2*pi*I\ ------- | 5 ___ 5 | ------ | 5 ___ 5 | ------ | 5 ___ 5 | ------ | 5 ___ 5 |
4/5 | \/ 3 *e | 4/5 5 | \/ 3 *e | 4/5 5 | \/ 3 *e | 4/5 5 | \/ 3 *e | 4/5 5 | \/ 3 *e |
/ 3 *Gamma(-1/5)*log|1 - -------------| 3 *e *Gamma(-1/5)*log|1 - -------------| 3 *e *Gamma(-1/5)*log|1 - -------------| 3 *e *Gamma(-1/5)*log|1 - -------------| 3 *e *Gamma(-1/5)*log|1 - -------------|
| | 5 _______ | | 5 _______ | | 5 _______ | | 5 _______ | | 5 _______ |
| 1 \ \/ 3 + x / \ \/ 3 + x / \ \/ 3 + x / \ \/ 3 + x / \ \/ 3 + x /
| ----------- dx = C - --------------------------------------- - ------------------------------------------------ - ----------------------------------------------- - ----------------------------------------------- + -----------------------------------------------
| 5 _______ 15*Gamma(4/5) 15*Gamma(4/5) 15*Gamma(4/5) 15*Gamma(4/5) 15*Gamma(4/5)
| x*\/ x + 3
|
/
$$\int \frac{1}{x \sqrt[5]{x + 3}}\, dx = C + \frac{3^{\frac{4}{5}} e^{\frac{3 i \pi}{5}} \log{\left(1 - \frac{\sqrt[5]{3} e^{\frac{2 i \pi}{5}}}{\sqrt[5]{x + 3}} \right)} \Gamma\left(- \frac{1}{5}\right)}{15 \Gamma\left(\frac{4}{5}\right)} - \frac{3^{\frac{4}{5}} e^{- \frac{4 i \pi}{5}} \log{\left(1 - \frac{\sqrt[5]{3} e^{\frac{4 i \pi}{5}}}{\sqrt[5]{x + 3}} \right)} \Gamma\left(- \frac{1}{5}\right)}{15 \Gamma\left(\frac{4}{5}\right)} - \frac{3^{\frac{4}{5}} e^{\frac{4 i \pi}{5}} \log{\left(1 - \frac{\sqrt[5]{3} e^{\frac{6 i \pi}{5}}}{\sqrt[5]{x + 3}} \right)} \Gamma\left(- \frac{1}{5}\right)}{15 \Gamma\left(\frac{4}{5}\right)} - \frac{3^{\frac{4}{5}} e^{\frac{2 i \pi}{5}} \log{\left(1 - \frac{\sqrt[5]{3} e^{\frac{8 i \pi}{5}}}{\sqrt[5]{x + 3}} \right)} \Gamma\left(- \frac{1}{5}\right)}{15 \Gamma\left(\frac{4}{5}\right)} - \frac{3^{\frac{4}{5}} \log{\left(1 - \frac{\sqrt[5]{3} e^{2 i \pi}}{\sqrt[5]{x + 3}} \right)} \Gamma\left(- \frac{1}{5}\right)}{15 \Gamma\left(\frac{4}{5}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.