Sr Examen
Integral de dx/√(5-x^3) dx
Solución
Ha introducido
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1 / | | 1 | ----------- dx | ________ | / 3 | \/ 5 - x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{5 - x^{3}}}\, dx$$
Integral(1/(sqrt(5 - x^3)), (x, 0, 1))
Respuesta (Indefinida)
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_ / | 3 2*pi*I\
/ ___ |_ |1/3, 1/2 | x *e |
| x*\/ 5 *Gamma(1/3)* | | | ----------|
| 1 2 1 \ 4/3 | 5 /
| ----------- dx = C + -----------------------------------------------
| ________ 15*Gamma(4/3)
| / 3
| \/ 5 - x
|
/
$$\int \frac{1}{\sqrt{5 - x^{3}}}\, dx = C + \frac{\sqrt{5} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{2 i \pi}}{5}} \right)}}{15 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
_
___ |_ /1/3, 1/2 | \
\/ 5 *Gamma(1/3)* | | | 1/5|
2 1 \ 4/3 | /
--------------------------------------
15*Gamma(4/3)
$$\frac{\sqrt{5} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1}{5}} \right)}}{15 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_
___ |_ /1/3, 1/2 | \
\/ 5 *Gamma(1/3)* | | | 1/5|
2 1 \ 4/3 | /
--------------------------------------
15*Gamma(4/3)
$$\frac{\sqrt{5} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1}{5}} \right)}}{15 \Gamma\left(\frac{4}{3}\right)}$$
sqrt(5)*gamma(1/3)*hyper((1/3, 1/2), (4/3,), 1/5)/(15*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.