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