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