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