Sr Examen
Integral de x/sqrt(x^10+10) dx
Solución
Ha introducido
[src]
oo / | | x | ------------- dx | __________ | / 10 | \/ x + 10 | / 1
$$\int\limits_{1}^{\infty} \frac{x}{\sqrt{x^{10} + 10}}\, dx$$
Integral(x/sqrt(x^10 + 10), (x, 1, oo))
Respuesta (Indefinida)
[src]
_ / | 10 pi*I\
/ ____ 2 |_ |1/5, 1/2 | x *e |
| \/ 10 *x *Gamma(1/5)* | | | ---------|
| x 2 1 \ 6/5 | 10 /
| ------------- dx = C + ------------------------------------------------
| __________ 100*Gamma(6/5)
| / 10
| \/ x + 10
|
/
$$\int \frac{x}{\sqrt{x^{10} + 10}}\, dx = C + \frac{\sqrt{10} x^{2} \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{2} \\ \frac{6}{5} \end{matrix}\middle| {\frac{x^{10} e^{i \pi}}{10}} \right)}}{100 \Gamma\left(\frac{6}{5}\right)}$$
Respuesta
[src]
_ /3/10, 1/2 | \
|_ | | pi*I|
Gamma(3/10)* | | 13 | 10*e |
2 1 | -- | |
\ 10 | /
---------------------------------------
/13\
10*Gamma|--|
\10/
$$\frac{\Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{10}, \frac{1}{2} \\ \frac{13}{10} \end{matrix}\middle| {10 e^{i \pi}} \right)}}{10 \Gamma\left(\frac{13}{10}\right)}$$
=
=
_ /3/10, 1/2 | \
|_ | | pi*I|
Gamma(3/10)* | | 13 | 10*e |
2 1 | -- | |
\ 10 | /
---------------------------------------
/13\
10*Gamma|--|
\10/
$$\frac{\Gamma\left(\frac{3}{10}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{10}, \frac{1}{2} \\ \frac{13}{10} \end{matrix}\middle| {10 e^{i \pi}} \right)}}{10 \Gamma\left(\frac{13}{10}\right)}$$
gamma(3/10)*hyper((3/10, 1/2), (13/10,), 10*exp_polar(pi*i))/(10*gamma(13/10))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.