Sr Examen
Integral de (x^4+5)^(-1/2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | ________ | / 4 | \/ x + 5 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x^{4} + 5}}\, dx$$
Integral(1/sqrt(x^4 + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 4 pi*I\
/ ___ |_ |1/4, 1/2 | x *e |
| x*\/ 5 *Gamma(1/4)* | | | --------|
| 1 2 1 \ 5/4 | 5 /
| ----------- dx = C + ---------------------------------------------
| ________ 20*Gamma(5/4)
| / 4
| \/ x + 5
|
/
$$\int \frac{1}{\sqrt{x^{4} + 5}}\, dx = C + \frac{\sqrt{5} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4} e^{i \pi}}{5}} \right)}}{20 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
_
___ |_ /1/4, 1/2 | \
\/ 5 *Gamma(1/4)* | | | -1/5|
2 1 \ 5/4 | /
---------------------------------------
20*Gamma(5/4)
$$\frac{\sqrt{5} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{5}} \right)}}{20 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_
___ |_ /1/4, 1/2 | \
\/ 5 *Gamma(1/4)* | | | -1/5|
2 1 \ 5/4 | /
---------------------------------------
20*Gamma(5/4)
$$\frac{\sqrt{5} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{5}} \right)}}{20 \Gamma\left(\frac{5}{4}\right)}$$
sqrt(5)*gamma(1/4)*hyper((1/4, 1/2), (5/4,), -1/5)/(20*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.