Sr Examen
Integral de |sh3x|*e^((i*n*pi*x)/2) dx
Solución
Ha introducido
[src]
1 / | | I*n*pi*x | -------- | 2 | |sinh(3*x)|*E dx | / 0
$$\int\limits_{0}^{1} e^{\frac{x \pi i n}{2}} \left|{\sinh{\left(3 x \right)}}\right|\, dx$$
Integral(Abs(sinh(3*x))*E^((((i*n)*pi)*x)/2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / | | | I*n*pi*x | pi*I*n*x | -------- | -------- | 2 | 2 | |sinh(3*x)|*E dx = C + | |sinh(3*x)|*e dx | | / /
$$\int e^{\frac{x \pi i n}{2}} \left|{\sinh{\left(3 x \right)}}\right|\, dx = C + \int e^{\frac{i \pi n x}{2}} \left|{\sinh{\left(3 x \right)}}\right|\, dx$$
Respuesta
[src]
pi*I*n pi*I*n
------ ------
2 2
12 12*cosh(3)*e 2*pi*I*n*e *sinh(3)
- ----------- + ------------------ - ------------------------
2 2 2 2 2 2
36 + pi *n 36 + pi *n 36 + pi *n
$$- \frac{2 i \pi n e^{\frac{i \pi n}{2}} \sinh{\left(3 \right)}}{\pi^{2} n^{2} + 36} + \frac{12 e^{\frac{i \pi n}{2}} \cosh{\left(3 \right)}}{\pi^{2} n^{2} + 36} - \frac{12}{\pi^{2} n^{2} + 36}$$
=
=
pi*I*n pi*I*n
------ ------
2 2
12 12*cosh(3)*e 2*pi*I*n*e *sinh(3)
- ----------- + ------------------ - ------------------------
2 2 2 2 2 2
36 + pi *n 36 + pi *n 36 + pi *n
$$- \frac{2 i \pi n e^{\frac{i \pi n}{2}} \sinh{\left(3 \right)}}{\pi^{2} n^{2} + 36} + \frac{12 e^{\frac{i \pi n}{2}} \cosh{\left(3 \right)}}{\pi^{2} n^{2} + 36} - \frac{12}{\pi^{2} n^{2} + 36}$$
-12/(36 + pi^2*n^2) + 12*cosh(3)*exp(pi*i*n/2)/(36 + pi^2*n^2) - 2*pi*i*n*exp(pi*i*n/2)*sinh(3)/(36 + pi^2*n^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.