Sr Examen
Integral de e^(x)*sin(n*x) dx
Solución
Ha introducido
[src]
x / | | x | E *sin(n*x) dx | / 0
$$\int\limits_{0}^{x} e^{x} \sin{\left(n x \right)}\, dx$$
Integral(E^x*sin(n*x), (x, 0, x))
Respuesta (Indefinida)
[src]
// / x x x\ \
|| |e *sinh(x) x*e *sinh(x) x*cosh(x)*e | |
||-I*|---------- + ------------ - ------------| for n = -I|
|| \ 2 2 2 / |
/ || |
| || / x x x\ |
| x || |e *sinh(x) x*e *sinh(x) x*cosh(x)*e | |
| E *sin(n*x) dx = C + |
$$\int e^{x} \sin{\left(n x \right)}\, dx = C + \begin{cases} - i \left(\frac{x e^{x} \sinh{\left(x \right)}}{2} - \frac{x e^{x} \cosh{\left(x \right)}}{2} + \frac{e^{x} \sinh{\left(x \right)}}{2}\right) & \text{for}\: n = - i \\i \left(\frac{x e^{x} \sinh{\left(x \right)}}{2} - \frac{x e^{x} \cosh{\left(x \right)}}{2} + \frac{e^{x} \sinh{\left(x \right)}}{2}\right) & \text{for}\: n = i \\- \frac{n e^{x} \cos{\left(n x \right)}}{n^{2} + 1} + \frac{e^{x} \sin{\left(n x \right)}}{n^{2} + 1} & \text{otherwise} \end{cases}$$
Respuesta
[src]
x x
n e *sin(n*x) n*cos(n*x)*e
------ + ----------- - -------------
2 2 2
1 + n 1 + n 1 + n
$$- \frac{n e^{x} \cos{\left(n x \right)}}{n^{2} + 1} + \frac{n}{n^{2} + 1} + \frac{e^{x} \sin{\left(n x \right)}}{n^{2} + 1}$$
=
=
x x
n e *sin(n*x) n*cos(n*x)*e
------ + ----------- - -------------
2 2 2
1 + n 1 + n 1 + n
$$- \frac{n e^{x} \cos{\left(n x \right)}}{n^{2} + 1} + \frac{n}{n^{2} + 1} + \frac{e^{x} \sin{\left(n x \right)}}{n^{2} + 1}$$
n/(1 + n^2) + exp(x)*sin(n*x)/(1 + n^2) - n*cos(n*x)*exp(x)/(1 + n^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.