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