Sr Examen
Integral de (81+x^4)^(-1/4) dx
Solución
Ha introducido
[src]
3/2 / | | 1 | ------------ dx | _________ | 4 / 4 | \/ 81 + x | / 0
$$\int\limits_{0}^{\frac{3}{2}} \frac{1}{\sqrt[4]{x^{4} + 81}}\, dx$$
Integral((81 + x^4)^(-1/4), (x, 0, 3/2))
Respuesta (Indefinida)
[src]
_ / | 4 pi*I\
/ |_ |1/4, 1/4 | x *e |
| x*Gamma(1/4)* | | | --------|
| 1 2 1 \ 5/4 | 81 /
| ------------ dx = C + ---------------------------------------
| _________ 12*Gamma(5/4)
| 4 / 4
| \/ 81 + x
|
/
$$\int \frac{1}{\sqrt[4]{x^{4} + 81}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4} e^{i \pi}}{81}} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /1/4, 1/4 | \
Gamma(1/4)* | | | -1/16|
2 1 \ 5/4 | /
----------------------------------
8*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{16}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_
|_ /1/4, 1/4 | \
Gamma(1/4)* | | | -1/16|
2 1 \ 5/4 | /
----------------------------------
8*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{16}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}$$
gamma(1/4)*hyper((1/4, 1/4), (5/4,), -1/16)/(8*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.