Sr Examen
Integral de 1/sqrt(3+x^8) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | ________ | / 8 | \/ 3 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x^{8} + 3}}\, dx$$
Integral(1/(sqrt(3 + x^8)), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 8 pi*I\
/ ___ |_ |1/8, 1/2 | x *e |
| x*\/ 3 *Gamma(1/8)* | | | --------|
| 1 2 1 \ 9/8 | 3 /
| ----------- dx = C + ---------------------------------------------
| ________ 24*Gamma(9/8)
| / 8
| \/ 3 + x
|
/
$$\int \frac{1}{\sqrt{x^{8} + 3}}\, dx = C + \frac{\sqrt{3} x \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{1}{2} \\ \frac{9}{8} \end{matrix}\middle| {\frac{x^{8} e^{i \pi}}{3}} \right)}}{24 \Gamma\left(\frac{9}{8}\right)}$$
Gráfica
Respuesta
[src]
_
___ |_ /1/8, 1/2 | \
\/ 3 *Gamma(1/8)* | | | -1/3|
2 1 \ 9/8 | /
---------------------------------------
24*Gamma(9/8)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{1}{2} \\ \frac{9}{8} \end{matrix}\middle| {- \frac{1}{3}} \right)}}{24 \Gamma\left(\frac{9}{8}\right)}$$
=
=
_
___ |_ /1/8, 1/2 | \
\/ 3 *Gamma(1/8)* | | | -1/3|
2 1 \ 9/8 | /
---------------------------------------
24*Gamma(9/8)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{1}{2} \\ \frac{9}{8} \end{matrix}\middle| {- \frac{1}{3}} \right)}}{24 \Gamma\left(\frac{9}{8}\right)}$$
sqrt(3)*gamma(1/8)*hyper((1/8, 1/2), (9/8,), -1/3)/(24*gamma(9/8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.