Integral de (a^(2/3)-x^(2/3))^(4/3) dx
Solución
Respuesta (Indefinida)
[src]
_ / | 2/3 2*pi*I\
/ 2/9 5/3 |_ |-1/3, 5/2 | x *e |
| 3*a *x * | | | ------------|
| 4/3 _ / | 2/3 2*pi*I\ 2 1 | 7/2 | 2/3 |
| / 2/3 2/3\ 8/9 |_ |-1/3, 3/2 | x *e | \ | a /
| \a - x / dx = C + x*a * | | | ------------| - -------------------------------------------
| 2 1 | 5/2 | 2/3 | 5
/ \ | a /
$$\int \left(a^{\frac{2}{3}} - x^{\frac{2}{3}}\right)^{\frac{4}{3}}\, dx = C + a^{\frac{8}{9}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{x^{\frac{2}{3}} e^{2 i \pi}}{a^{\frac{2}{3}}}} \right)} - \frac{3 a^{\frac{2}{9}} x^{\frac{5}{3}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{x^{\frac{2}{3}} e^{2 i \pi}}{a^{\frac{2}{3}}}} \right)}}{5}$$
_
17/9 |_ /-4/3, 3/2 | \
a * | | | 1|
2 1 \ 5/2 | /
$$a^{\frac{17}{9}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {1} \right)}$$
=
_
17/9 |_ /-4/3, 3/2 | \
a * | | | 1|
2 1 \ 5/2 | /
$$a^{\frac{17}{9}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{4}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {1} \right)}$$
a^(17/9)*hyper((-4/3, 3/2), (5/2,), 1)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.