Sr Examen
Integral de (cos(4x))/x^(1/9) dx
Solución
Ha introducido
[src]
oo / | | cos(4*x) | -------- dx | 9 ___ | \/ x | / 1
$$\int\limits_{1}^{\infty} \frac{\cos{\left(4 x \right)}}{\sqrt[9]{x}}\, dx$$
Integral(cos(4*x)/x^(1/9), (x, 1, oo))
Respuesta
[src]
/ _ \
| |_ / 4/9 | \|
|9 ___ Gamma(-4/9)* | | | -4||
____ |\/ 2 *Gamma(4/9) 1 2 \1/2, 13/9 | /|
\/ pi *|---------------- + ---------------------------------|
| 2*Gamma(1/18) ____ |
\ \/ pi *Gamma(5/9) /
-------------------------------------------------------------
2
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{4}{9}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{4}{9} \\ \frac{1}{2}, \frac{13}{9} \end{matrix}\middle| {-4} \right)}}{\sqrt{\pi} \Gamma\left(\frac{5}{9}\right)} + \frac{\sqrt[9]{2} \Gamma\left(\frac{4}{9}\right)}{2 \Gamma\left(\frac{1}{18}\right)}\right)}{2}$$
=
=
/ _ \
| |_ / 4/9 | \|
|9 ___ Gamma(-4/9)* | | | -4||
____ |\/ 2 *Gamma(4/9) 1 2 \1/2, 13/9 | /|
\/ pi *|---------------- + ---------------------------------|
| 2*Gamma(1/18) ____ |
\ \/ pi *Gamma(5/9) /
-------------------------------------------------------------
2
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{4}{9}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{4}{9} \\ \frac{1}{2}, \frac{13}{9} \end{matrix}\middle| {-4} \right)}}{\sqrt{\pi} \Gamma\left(\frac{5}{9}\right)} + \frac{\sqrt[9]{2} \Gamma\left(\frac{4}{9}\right)}{2 \Gamma\left(\frac{1}{18}\right)}\right)}{2}$$
sqrt(pi)*(2^(1/9)*gamma(4/9)/(2*gamma(1/18)) + gamma(-4/9)*hyper((4/9,), (1/2, 13/9), -4)/(sqrt(pi)*gamma(5/9)))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.