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