Sr Examen
Integral de x/sqrt(x^7+2) dx
Solución
Ha introducido
[src]
oo / | | x | ----------- dx | ________ | / 7 | \/ x + 2 | / 1
$$\int\limits_{1}^{\infty} \frac{x}{\sqrt{x^{7} + 2}}\, dx$$
Integral(x/sqrt(x^7 + 2), (x, 1, oo))
Respuesta (Indefinida)
[src]
_ / | 7 pi*I\
/ ___ 2 |_ |2/7, 1/2 | x *e |
| \/ 2 *x *Gamma(2/7)* | | | --------|
| x 2 1 \ 9/7 | 2 /
| ----------- dx = C + ----------------------------------------------
| ________ 14*Gamma(9/7)
| / 7
| \/ x + 2
|
/
$$\int \frac{x}{\sqrt{x^{7} + 2}}\, dx = C + \frac{\sqrt{2} x^{2} \Gamma\left(\frac{2}{7}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{7}, \frac{1}{2} \\ \frac{9}{7} \end{matrix}\middle| {\frac{x^{7} e^{i \pi}}{2}} \right)}}{14 \Gamma\left(\frac{9}{7}\right)}$$
Respuesta
[src]
_ /3/14, 1/2 | \
|_ | | pi*I|
Gamma(3/14)* | | 17 | 2*e |
2 1 | -- | |
\ 14 | /
--------------------------------------
/17\
7*Gamma|--|
\14/
$$\frac{\Gamma\left(\frac{3}{14}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{14}, \frac{1}{2} \\ \frac{17}{14} \end{matrix}\middle| {2 e^{i \pi}} \right)}}{7 \Gamma\left(\frac{17}{14}\right)}$$
=
=
_ /3/14, 1/2 | \
|_ | | pi*I|
Gamma(3/14)* | | 17 | 2*e |
2 1 | -- | |
\ 14 | /
--------------------------------------
/17\
7*Gamma|--|
\14/
$$\frac{\Gamma\left(\frac{3}{14}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{14}, \frac{1}{2} \\ \frac{17}{14} \end{matrix}\middle| {2 e^{i \pi}} \right)}}{7 \Gamma\left(\frac{17}{14}\right)}$$
gamma(3/14)*hyper((3/14, 1/2), (17/14,), 2*exp_polar(pi*i))/(7*gamma(17/14))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.