Sr Examen
Integral de 1/(1+x^8)^(1/2) dx
Solución
Ha introducido
[src]
oo / | | 1 | ----------- dx | ________ | / 8 | \/ 1 + x | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\sqrt{x^{8} + 1}}\, dx$$
Integral(1/(sqrt(1 + x^8)), (x, 2, oo))
Respuesta (Indefinida)
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_ / |_ /1/8, 1/2 | 8 pi*I\ | x*Gamma(1/8)* | | | x *e | | 1 2 1 \ 9/8 | / | ----------- dx = C + --------------------------------------- | ________ 8*Gamma(9/8) | / 8 | \/ 1 + x | /
$$\int \frac{1}{\sqrt{x^{8} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{8}, \frac{1}{2} \\ \frac{9}{8} \end{matrix}\middle| {x^{8} e^{i \pi}} \right)}}{8 \Gamma\left(\frac{9}{8}\right)}$$
Respuesta
[src]
_
|_ /3/8, 1/2 | \
Gamma(3/8)* | | | -1/256|
2 1 \ 11/8 | /
-----------------------------------
64*Gamma(11/8)
$$\frac{\Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {- \frac{1}{256}} \right)}}{64 \Gamma\left(\frac{11}{8}\right)}$$
=
=
_
|_ /3/8, 1/2 | \
Gamma(3/8)* | | | -1/256|
2 1 \ 11/8 | /
-----------------------------------
64*Gamma(11/8)
$$\frac{\Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {- \frac{1}{256}} \right)}}{64 \Gamma\left(\frac{11}{8}\right)}$$
gamma(3/8)*hyper((3/8, 1/2), (11/8,), -1/256)/(64*gamma(11/8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.