Integral de cos(t)*e^(t*(-p)) dt
Solución
Respuesta (Indefinida)
[src]
// I*t I*t I*t \
|| t*cos(t)*e I*cos(t)*e I*t*e *sin(t) |
|| ------------- - ------------- - --------------- for p = -I|
|| 2 2 2 |
/ || |
| || -I*t -I*t -I*t |
| t*(-p) ||I*cos(t)*e t*cos(t)*e I*t*e *sin(t) |
| cos(t)*E dt = C + |<-------------- + -------------- + ---------------- for p = I |
| || 2 2 2 |
/ || |
|| sin(t) p*cos(t) |
|| -------------- - -------------- otherwise |
|| 2 p*t p*t 2 p*t p*t |
|| p *e + e p *e + e |
\\ /
∫e−ptcos(t)dt=C+⎩⎨⎧−2iteitsin(t)+2teitcos(t)−2ieitcos(t)2ite−itsin(t)+2te−itcos(t)+2ie−itcos(t)−p2ept+eptpcos(t)+p2ept+eptsin(t)forp=−iforp=iotherwise
/ p
| ------ for 2*|arg(p)| < pi
| 2
| 1 + p
|
| oo
< /
| |
| | -p*t
| | cos(t)*e dt otherwise
| |
|/
\0
⎩⎨⎧p2+1p0∫∞e−ptcos(t)dtfor2∣arg(p)∣<πotherwise
=
/ p
| ------ for 2*|arg(p)| < pi
| 2
| 1 + p
|
| oo
< /
| |
| | -p*t
| | cos(t)*e dt otherwise
| |
|/
\0
⎩⎨⎧p2+1p0∫∞e−ptcos(t)dtfor2∣arg(p)∣<πotherwise
Piecewise((p/(1 + p^2), 2*Abs(arg(p)) < pi), (Integral(cos(t)*exp(-p*t), (t, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.