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