Sr Examen
Integral de dx/x*(x+3)^(1/5) dx
Solución
Ha introducido
[src]
oo / | | 5 _______ | \/ x + 3 | --------- dx | x | / 0
$$\int\limits_{0}^{\infty} \frac{\sqrt[5]{x + 3}}{x}\, dx$$
Integral((x + 3)^(1/5)/x, (x, 0, oo))
Respuesta (Indefinida)
[src]
/ 4*pi*I\ / 2*pi*I\ / 8*pi*I\ / 6*pi*I\
-4*pi*I | ------| -2*pi*I | ------| 2*pi*I | ------| 4*pi*I | ------|
/ / 4/5 5 _______\ ------- | 4/5 5 _______ 5 | ------- | 4/5 5 _______ 5 | ------ | 4/5 5 _______ 5 | ------ | 4/5 5 _______ 5 |
| 5 ___ | 3 *\/ 3 + x | 5 ___ 5 | 3 *\/ 3 + x *e | 5 ___ 5 | 3 *\/ 3 + x *e | 5 ___ 5 | 3 *\/ 3 + x *e | 5 ___ 5 | 3 *\/ 3 + x *e |
| 5 _______ 5 _______ 6*\/ 3 *Gamma(6/5)*log|1 - --------------| 6*\/ 3 *e *Gamma(6/5)*log|1 - ----------------------| 6*\/ 3 *e *Gamma(6/5)*log|1 - ----------------------| 6*\/ 3 *e *Gamma(6/5)*log|1 - ----------------------| 6*\/ 3 *e *Gamma(6/5)*log|1 - ----------------------|
| \/ x + 3 6*\/ 3 + x *Gamma(6/5) \ 3 / \ 3 / \ 3 / \ 3 / \ 3 /
| --------- dx = C + ---------------------- + ------------------------------------------ + ----------------------------------------------------------- + ----------------------------------------------------------- + ---------------------------------------------------------- + ----------------------------------------------------------
| x Gamma(11/5) 5*Gamma(11/5) 5*Gamma(11/5) 5*Gamma(11/5) 5*Gamma(11/5) 5*Gamma(11/5)
|
/
$$\int \frac{\sqrt[5]{x + 3}}{x}\, dx = C + \frac{6 \sqrt[5]{x + 3} \Gamma\left(\frac{6}{5}\right)}{\Gamma\left(\frac{11}{5}\right)} + \frac{6 \sqrt[5]{3} \log{\left(- \frac{3^{\frac{4}{5}} \sqrt[5]{x + 3}}{3} + 1 \right)} \Gamma\left(\frac{6}{5}\right)}{5 \Gamma\left(\frac{11}{5}\right)} + \frac{6 \sqrt[5]{3} e^{- \frac{2 i \pi}{5}} \log{\left(- \frac{3^{\frac{4}{5}} \sqrt[5]{x + 3} e^{\frac{2 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{6}{5}\right)}{5 \Gamma\left(\frac{11}{5}\right)} + \frac{6 \sqrt[5]{3} e^{- \frac{4 i \pi}{5}} \log{\left(- \frac{3^{\frac{4}{5}} \sqrt[5]{x + 3} e^{\frac{4 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{6}{5}\right)}{5 \Gamma\left(\frac{11}{5}\right)} + \frac{6 \sqrt[5]{3} e^{\frac{4 i \pi}{5}} \log{\left(- \frac{3^{\frac{4}{5}} \sqrt[5]{x + 3} e^{\frac{6 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{6}{5}\right)}{5 \Gamma\left(\frac{11}{5}\right)} + \frac{6 \sqrt[5]{3} e^{\frac{2 i \pi}{5}} \log{\left(- \frac{3^{\frac{4}{5}} \sqrt[5]{x + 3} e^{\frac{8 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{6}{5}\right)}{5 \Gamma\left(\frac{11}{5}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.