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