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