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