Respuesta (Indefinida)
[src]
/ // a*t \
| || -e |
| -s*t a*t ||--------------- for a != s|
| E *E dt = C + |< s*t s*t |
| ||s*e - a*e |
/ || |
\\ t otherwise /
$$\int e^{a t} e^{- s t}\, dt = C + \begin{cases} - \frac{e^{a t}}{- a e^{s t} + s e^{s t}} & \text{for}\: a \neq s \\t & \text{otherwise} \end{cases}$$
/ -1 / / pi pi\ / pi pi\ / pi pi\\
| --------- for Or|And||arg(s)| <= --, |pi + arg(a)| < --|, And||pi + arg(a)| <= --, |arg(s)| < --|, And||pi + arg(a)| < --, |arg(s)| < --||
| / s\ \ \ 2 2 / \ 2 2 / \ 2 2 //
| a*|1 - -|
| \ a/
|
| oo
< /
| |
| | a*t -s*t
| | e *e dt otherwise
| |
|/
|0
\
$$\begin{cases} - \frac{1}{a \left(1 - \frac{s}{a}\right)} & \text{for}\: \left(\left|{\arg{\left(s \right)}}\right| \leq \frac{\pi}{2} \wedge \left|{\arg{\left(a \right)} + \pi}\right| < \frac{\pi}{2}\right) \vee \left(\left|{\arg{\left(a \right)} + \pi}\right| \leq \frac{\pi}{2} \wedge \left|{\arg{\left(s \right)}}\right| < \frac{\pi}{2}\right) \vee \left(\left|{\arg{\left(a \right)} + \pi}\right| < \frac{\pi}{2} \wedge \left|{\arg{\left(s \right)}}\right| < \frac{\pi}{2}\right) \\\int\limits_{0}^{\infty} e^{a t} e^{- s t}\, dt & \text{otherwise} \end{cases}$$
=
/ -1 / / pi pi\ / pi pi\ / pi pi\\
| --------- for Or|And||arg(s)| <= --, |pi + arg(a)| < --|, And||pi + arg(a)| <= --, |arg(s)| < --|, And||pi + arg(a)| < --, |arg(s)| < --||
| / s\ \ \ 2 2 / \ 2 2 / \ 2 2 //
| a*|1 - -|
| \ a/
|
| oo
< /
| |
| | a*t -s*t
| | e *e dt otherwise
| |
|/
|0
\
$$\begin{cases} - \frac{1}{a \left(1 - \frac{s}{a}\right)} & \text{for}\: \left(\left|{\arg{\left(s \right)}}\right| \leq \frac{\pi}{2} \wedge \left|{\arg{\left(a \right)} + \pi}\right| < \frac{\pi}{2}\right) \vee \left(\left|{\arg{\left(a \right)} + \pi}\right| \leq \frac{\pi}{2} \wedge \left|{\arg{\left(s \right)}}\right| < \frac{\pi}{2}\right) \vee \left(\left|{\arg{\left(a \right)} + \pi}\right| < \frac{\pi}{2} \wedge \left|{\arg{\left(s \right)}}\right| < \frac{\pi}{2}\right) \\\int\limits_{0}^{\infty} e^{a t} e^{- s t}\, dt & \text{otherwise} \end{cases}$$
Piecewise((-1/(a*(1 - s/a)), ((Abs(arg(s)) <= pi/2)∧(Abs(pi + arg(a)) < pi/2))∨((Abs(arg(s)) < pi/2)∧(Abs(pi + arg(a)) <= pi/2))∨((Abs(arg(s)) < pi/2)∧(Abs(pi + arg(a)) < pi/2))), (Integral(exp(a*t)*exp(-s*t), (t, 0, oo)), True))