Sr Examen
Integral de cos(x)/(x^(1/3)) dx
Solución
Ha introducido
[src]
oo / | | cos(x) | ------ dx | 3 ___ | \/ x | / 1
$$\int\limits_{1}^{\infty} \frac{\cos{\left(x \right)}}{\sqrt[3]{x}}\, dx$$
Integral(cos(x)/x^(1/3), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | cos(x) | cos(x) | ------ dx = C + | ------ dx | 3 ___ | 3 ___ | \/ x | \/ x | | / /
$$\int \frac{\cos{\left(x \right)}}{\sqrt[3]{x}}\, dx = C + \int \frac{\cos{\left(x \right)}}{\sqrt[3]{x}}\, dx$$
Respuesta
[src]
/ _ \
| |_ / 1/3 | \|
| 2/3 Gamma(-1/3)* | | | -1/4||
____ |2 *Gamma(1/3) 1 2 \1/2, 4/3 | /|
\/ pi *|--------------- + ----------------------------------|
| Gamma(1/6) ____ |
\ \/ pi *Gamma(2/3) /
-------------------------------------------------------------
2
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \Gamma\left(\frac{1}{3}\right)}{\Gamma\left(\frac{1}{6}\right)}\right)}{2}$$
=
=
/ _ \
| |_ / 1/3 | \|
| 2/3 Gamma(-1/3)* | | | -1/4||
____ |2 *Gamma(1/3) 1 2 \1/2, 4/3 | /|
\/ pi *|--------------- + ----------------------------------|
| Gamma(1/6) ____ |
\ \/ pi *Gamma(2/3) /
-------------------------------------------------------------
2
$$\frac{\sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{3} \\ \frac{1}{2}, \frac{4}{3} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{\sqrt{\pi} \Gamma\left(\frac{2}{3}\right)} + \frac{2^{\frac{2}{3}} \Gamma\left(\frac{1}{3}\right)}{\Gamma\left(\frac{1}{6}\right)}\right)}{2}$$
sqrt(pi)*(2^(2/3)*gamma(1/3)/gamma(1/6) + gamma(-1/3)*hyper((1/3,), (1/2, 4/3), -1/4)/(sqrt(pi)*gamma(2/3)))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.