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