Sr Examen
Integral de cbrt(1+x^5)x^2 dx
Solución
Ha introducido
[src]
1 / | | ________ | 3 / 5 2 | \/ 1 + x *x dx | / 0
$$\int\limits_{0}^{1} x^{2} \sqrt[3]{x^{5} + 1}\, dx$$
Integral((1 + x^5)^(1/3)*x^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ _ | 3 |_ /-1/3, 3/5 | 5 pi*I\ | ________ x *Gamma(3/5)* | | | x *e | | 3 / 5 2 2 1 \ 8/5 | / | \/ 1 + x *x dx = C + ----------------------------------------- | 5*Gamma(8/5) /
$$\int x^{2} \sqrt[3]{x^{5} + 1}\, dx = C + \frac{x^{3} \Gamma\left(\frac{3}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{5} \\ \frac{8}{5} \end{matrix}\middle| {x^{5} e^{i \pi}} \right)}}{5 \Gamma\left(\frac{8}{5}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /-1/3, 3/5 | \
Gamma(3/5)* | | | -1|
2 1 \ 8/5 | /
--------------------------------
5*Gamma(8/5)
$$\frac{\Gamma\left(\frac{3}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{5} \\ \frac{8}{5} \end{matrix}\middle| {-1} \right)}}{5 \Gamma\left(\frac{8}{5}\right)}$$
=
=
_
|_ /-1/3, 3/5 | \
Gamma(3/5)* | | | -1|
2 1 \ 8/5 | /
--------------------------------
5*Gamma(8/5)
$$\frac{\Gamma\left(\frac{3}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{5} \\ \frac{8}{5} \end{matrix}\middle| {-1} \right)}}{5 \Gamma\left(\frac{8}{5}\right)}$$
gamma(3/5)*hyper((-1/3, 3/5), (8/5,), -1)/(5*gamma(8/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.