Sr Examen
Integral de sin(nx)*e^(2x) dx
Solución
Ha introducido
[src]
1 / | | 2*x | sin(n*x)*E dx | / 0
$$\int\limits_{0}^{1} e^{2 x} \sin{\left(n x \right)}\, dx$$
Integral(sin(n*x)*E^(2*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / 2*x 2*x 2*x\ \
|| |e *sinh(2*x) x*e *sinh(2*x) x*cosh(2*x)*e | |
||-I*|-------------- + ---------------- - ----------------| for n = -2*I|
|| \ 4 2 2 / |
/ || |
| || / 2*x 2*x 2*x\ |
| 2*x || |e *sinh(2*x) x*e *sinh(2*x) x*cosh(2*x)*e | |
| sin(n*x)*E dx = C + |
$$\int e^{2 x} \sin{\left(n x \right)}\, dx = C + \begin{cases} - i \left(\frac{x e^{2 x} \sinh{\left(2 x \right)}}{2} - \frac{x e^{2 x} \cosh{\left(2 x \right)}}{2} + \frac{e^{2 x} \sinh{\left(2 x \right)}}{4}\right) & \text{for}\: n = - 2 i \\i \left(\frac{x e^{2 x} \sinh{\left(2 x \right)}}{2} - \frac{x e^{2 x} \cosh{\left(2 x \right)}}{2} + \frac{e^{2 x} \sinh{\left(2 x \right)}}{4}\right) & \text{for}\: n = 2 i \\- \frac{n e^{2 x} \cos{\left(n x \right)}}{n^{2} + 4} + \frac{2 e^{2 x} \sin{\left(n x \right)}}{n^{2} + 4} & \text{otherwise} \end{cases}$$
Respuesta
[src]
2 2
n 2*e *sin(n) n*cos(n)*e
------ + ----------- - -----------
2 2 2
4 + n 4 + n 4 + n
$$- \frac{n e^{2} \cos{\left(n \right)}}{n^{2} + 4} + \frac{n}{n^{2} + 4} + \frac{2 e^{2} \sin{\left(n \right)}}{n^{2} + 4}$$
=
=
2 2
n 2*e *sin(n) n*cos(n)*e
------ + ----------- - -----------
2 2 2
4 + n 4 + n 4 + n
$$- \frac{n e^{2} \cos{\left(n \right)}}{n^{2} + 4} + \frac{n}{n^{2} + 4} + \frac{2 e^{2} \sin{\left(n \right)}}{n^{2} + 4}$$
n/(4 + n^2) + 2*exp(2)*sin(n)/(4 + n^2) - n*cos(n)*exp(2)/(4 + n^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.