Sr Examen
Integral de x^2*cos(xn) dx
Solución
Ha introducido
[src]
1 / | | 2 / n\ | x *cos\x / dx | / 0
$$\int\limits_{0}^{1} x^{2} \cos{\left(x^{n} \right)}\, dx$$
Integral(x^2*cos(x^n), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 3 | \
_ | --- | 2*n |
3 / 3 \ |_ | 2*n | -x |
x *Gamma|---|* | | | ------|
/ \2*n/ 1 2 | 3 | 4 |
| |1/2, 1 + --- | |
| 2 / n\ \ 2*n | /
| x *cos\x / dx = C + ------------------------------------------
| / 3 \
/ 2*n*Gamma|1 + ---|
\ 2*n/
$$\int x^{2} \cos{\left(x^{n} \right)}\, dx = C + \frac{x^{3} \Gamma\left(\frac{3}{2 n}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{2 n} \\ \frac{1}{2}, 1 + \frac{3}{2 n} \end{matrix}\middle| {- \frac{x^{2 n}}{4}} \right)}}{2 n \Gamma\left(1 + \frac{3}{2 n}\right)}$$
Respuesta
[src]
/ 3 | \
_ | --- | |
/ 3 \ |_ | 2*n | |
Gamma|---|* | | | -1/4|
\2*n/ 1 2 | 3 | |
|1/2, 1 + --- | |
\ 2*n | /
-------------------------------------
/ 3 \
2*n*Gamma|1 + ---|
\ 2*n/
$$\frac{\Gamma\left(\frac{3}{2 n}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{2 n} \\ \frac{1}{2}, 1 + \frac{3}{2 n} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 n \Gamma\left(1 + \frac{3}{2 n}\right)}$$
=
=
/ 3 | \
_ | --- | |
/ 3 \ |_ | 2*n | |
Gamma|---|* | | | -1/4|
\2*n/ 1 2 | 3 | |
|1/2, 1 + --- | |
\ 2*n | /
-------------------------------------
/ 3 \
2*n*Gamma|1 + ---|
\ 2*n/
$$\frac{\Gamma\left(\frac{3}{2 n}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{2 n} \\ \frac{1}{2}, 1 + \frac{3}{2 n} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 n \Gamma\left(1 + \frac{3}{2 n}\right)}$$
gamma(3/(2*n))*hyper((3/(2*n),), (1/2, 1 + 3/(2*n)), -1/4)/(2*n*gamma(1 + 3/(2*n)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.