Sr Examen
Integral de ((e^x-1)^(1/4)) dx
Solución
Ha introducido
[src]
1 / | | ________ | 4 / x | \/ E - 1 dx | / 0
$$\int\limits_{0}^{1} \sqrt[4]{e^{x} - 1}\, dx$$
Integral((E^x - 1)^(1/4), (x, 0, 1))
Respuesta
[src]
-pi*I / 5*pi*I\ -pi*I / pi*I\ -pi*I / 3*pi*I\ -pi*I / 7*pi*I\
------ | ------| ------ | ----| ------ | ------| ------ | ------|
4 ________ 4 | 4 ________ 4 | 4 | 4 ________ 4 | 4 | 4 ________ 4 | 4 | 4 ________ 4 |
5*\/ -1 + E *Gamma(5/4) 5*e *Gamma(5/4)*log\1 - \/ -1 + E *e / 5*e *Gamma(5/4)*log\1 - \/ -1 + E *e / 5*I*e *Gamma(5/4)*log\1 - \/ -1 + E *e / 5*I*e *Gamma(5/4)*log\1 - \/ -1 + E *e /
----------------------- - ------------------------------------------------ + ---------------------------------------------- - -------------------------------------------------- + --------------------------------------------------
Gamma(9/4) 4*Gamma(9/4) 4*Gamma(9/4) 4*Gamma(9/4) 4*Gamma(9/4)
$$- \frac{5 e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[4]{-1 + e} e^{\frac{5 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 i e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[4]{-1 + e} e^{\frac{7 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt[4]{-1 + e} \Gamma\left(\frac{5}{4}\right)}{\Gamma\left(\frac{9}{4}\right)} + \frac{5 e^{- \frac{i \pi}{4}} \log{\left(1 - \sqrt[4]{-1 + e} e^{\frac{i \pi}{4}} \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{5 i e^{- \frac{i \pi}{4}} \log{\left(1 - \sqrt[4]{-1 + e} e^{\frac{3 i \pi}{4}} \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)}$$
=
=
-pi*I / 5*pi*I\ -pi*I / pi*I\ -pi*I / 3*pi*I\ -pi*I / 7*pi*I\
------ | ------| ------ | ----| ------ | ------| ------ | ------|
4 ________ 4 | 4 ________ 4 | 4 | 4 ________ 4 | 4 | 4 ________ 4 | 4 | 4 ________ 4 |
5*\/ -1 + E *Gamma(5/4) 5*e *Gamma(5/4)*log\1 - \/ -1 + E *e / 5*e *Gamma(5/4)*log\1 - \/ -1 + E *e / 5*I*e *Gamma(5/4)*log\1 - \/ -1 + E *e / 5*I*e *Gamma(5/4)*log\1 - \/ -1 + E *e /
----------------------- - ------------------------------------------------ + ---------------------------------------------- - -------------------------------------------------- + --------------------------------------------------
Gamma(9/4) 4*Gamma(9/4) 4*Gamma(9/4) 4*Gamma(9/4) 4*Gamma(9/4)
$$- \frac{5 e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[4]{-1 + e} e^{\frac{5 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 i e^{- \frac{i \pi}{4}} \log{\left(- \sqrt[4]{-1 + e} e^{\frac{7 i \pi}{4}} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt[4]{-1 + e} \Gamma\left(\frac{5}{4}\right)}{\Gamma\left(\frac{9}{4}\right)} + \frac{5 e^{- \frac{i \pi}{4}} \log{\left(1 - \sqrt[4]{-1 + e} e^{\frac{i \pi}{4}} \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{5 i e^{- \frac{i \pi}{4}} \log{\left(1 - \sqrt[4]{-1 + e} e^{\frac{3 i \pi}{4}} \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)}$$
5*(-1 + E)^(1/4)*gamma(5/4)/gamma(9/4) - 5*exp(-pi*i/4)*gamma(5/4)*log(1 - (-1 + E)^(1/4)*exp_polar(5*pi*i/4))/(4*gamma(9/4)) + 5*exp(-pi*i/4)*gamma(5/4)*log(1 - (-1 + E)^(1/4)*exp_polar(pi*i/4))/(4*gamma(9/4)) - 5*i*exp(-pi*i/4)*gamma(5/4)*log(1 - (-1 + E)^(1/4)*exp_polar(3*pi*i/4))/(4*gamma(9/4)) + 5*i*exp(-pi*i/4)*gamma(5/4)*log(1 - (-1 + E)^(1/4)*exp_polar(7*pi*i/4))/(4*gamma(9/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.