Sr Examen
Integral de xe^(-(k+5)x) dx
Solución
Ha introducido
[src]
oo / | | (-k - 5)*x | x*E dx | / 0
$$\int\limits_{0}^{\infty} e^{x \left(- k - 5\right)} x\, dx$$
Integral(x*E^((-k - 5)*x), (x, 0, oo))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for k = -5|
|| 2 |
/ || | // x for 5 + k = 0\
| ||/ x*(-5 - k) | || |
| (-k - 5)*x ||| e 2 | || x*(-5 - k) |
| x*E dx = C - |<|-------------- for 25 + k + 10*k != 0 | + x*|<-e |
| ||| 2 | ||------------- otherwise |
/ ||<25 + k + 10*k otherwise | || 5 + k |
||| | \\ /
||| -x |
||| ----- otherwise |
||\ 5 + k |
\\ /
$$\int e^{x \left(- k - 5\right)} x\, dx = C + x \left(\begin{cases} x & \text{for}\: k + 5 = 0 \\- \frac{e^{x \left(- k - 5\right)}}{k + 5} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: k = -5 \\\begin{cases} \frac{e^{x \left(- k - 5\right)}}{k^{2} + 10 k + 25} & \text{for}\: k^{2} + 10 k + 25 \neq 0 \\- \frac{x}{k + 5} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ -1 pi | ---------------- for |pi + arg(-5 - k)| < -- | (-5 - k)*(5 + k) 2 | | oo | / < | | | x*(-5 - k) | | x*e dx otherwise | | |/ |0 \
$$\begin{cases} - \frac{1}{\left(- k - 5\right) \left(k + 5\right)} & \text{for}\: \left|{\arg{\left(- k - 5 \right)} + \pi}\right| < \frac{\pi}{2} \\\int\limits_{0}^{\infty} x e^{x \left(- k - 5\right)}\, dx & \text{otherwise} \end{cases}$$
=
=
/ -1 pi | ---------------- for |pi + arg(-5 - k)| < -- | (-5 - k)*(5 + k) 2 | | oo | / < | | | x*(-5 - k) | | x*e dx otherwise | | |/ |0 \
$$\begin{cases} - \frac{1}{\left(- k - 5\right) \left(k + 5\right)} & \text{for}\: \left|{\arg{\left(- k - 5 \right)} + \pi}\right| < \frac{\pi}{2} \\\int\limits_{0}^{\infty} x e^{x \left(- k - 5\right)}\, dx & \text{otherwise} \end{cases}$$
Piecewise((-1/((-5 - k)*(5 + k)), Abs(pi + arg(-5 - k)) < pi/2), (Integral(x*exp(x*(-5 - k)), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.