Sr Examen
Integral de ((x+1)/(x-1))^(1/3)*1/(x+1) dx
Solución
Ha introducido
[src]
1 / | | _______ | / x + 1 | 3 / ----- | \/ x - 1 | ----------- dx | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt[3]{\frac{x + 1}{x - 1}}}{x + 1}\, dx$$
Integral(((x + 1)/(x - 1))^(1/3)/(x + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / | | | _______ | ________ | / x + 1 | / 1 + x | 3 / ----- | 3 / ------ | \/ x - 1 | \/ -1 + x | ----------- dx = C + | ------------ dx | x + 1 | 1 + x | | / /
$$\int \frac{\sqrt[3]{\frac{x + 1}{x - 1}}}{x + 1}\, dx = C + \int \frac{\sqrt[3]{\frac{x + 1}{x - 1}}}{x + 1}\, dx$$
Respuesta
[src]
_
2/3 3 ___ |_ /2/3, 2/3 | \
-(-1) *\/ 2 *Gamma(2/3)* | | | 1/2|
2 1 \ 5/3 | /
------------------------------------------------
2*Gamma(5/3)
$$- \frac{\left(-1\right)^{\frac{2}{3}} \sqrt[3]{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{1}{2}} \right)}}{2 \Gamma\left(\frac{5}{3}\right)}$$
=
=
_
2/3 3 ___ |_ /2/3, 2/3 | \
-(-1) *\/ 2 *Gamma(2/3)* | | | 1/2|
2 1 \ 5/3 | /
------------------------------------------------
2*Gamma(5/3)
$$- \frac{\left(-1\right)^{\frac{2}{3}} \sqrt[3]{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{1}{2}} \right)}}{2 \Gamma\left(\frac{5}{3}\right)}$$
-(-1)^(2/3)*2^(1/3)*gamma(2/3)*hyper((2/3, 2/3), (5/3,), 1/2)/(2*gamma(5/3))
Respuesta numérica
[src]
(0.560326091837038 + 0.970513259868255j)
(0.560326091837038 + 0.970513259868255j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.