Sr Examen
Integral de 1/(x^(-4)+c)^0.5 dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------- dx | ________ | / 1 | / -- + c | / 4 | \/ x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{c + \frac{1}{x^{4}}}}\, dx$$
Integral(1/(sqrt(x^(-4) + c)), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | pi*I\
|_ |-1/4, 1/2 | e |
/ x*Gamma(-1/4)* | | | -----|
| 2 1 | 3/4 | 4|
| 1 \ | c*x /
| ------------- dx = C - --------------------------------------
| ________ ___
| / 1 4*\/ c *Gamma(3/4)
| / -- + c
| / 4
| \/ x
|
/
$$\int \frac{1}{\sqrt{c + \frac{1}{x^{4}}}}\, dx = C - \frac{x \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{e^{i \pi}}{c x^{4}}} \right)}}{4 \sqrt{c} \Gamma\left(\frac{3}{4}\right)}$$
Respuesta
[src]
_ / | pi*I\
|_ |-1/4, 1/2 | e |
-Gamma(-1/4)* | | | -----|
2 1 \ 3/4 | c /
--------------------------------------
___
4*\/ c *Gamma(3/4)
$$- \frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{e^{i \pi}}{c}} \right)}}{4 \sqrt{c} \Gamma\left(\frac{3}{4}\right)}$$
=
=
_ / | pi*I\
|_ |-1/4, 1/2 | e |
-Gamma(-1/4)* | | | -----|
2 1 \ 3/4 | c /
--------------------------------------
___
4*\/ c *Gamma(3/4)
$$- \frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {\frac{e^{i \pi}}{c}} \right)}}{4 \sqrt{c} \Gamma\left(\frac{3}{4}\right)}$$
-gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), exp_polar(pi*i)/c)/(4*sqrt(c)*gamma(3/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.