Integral de t*cos(t)*e^(-st) dt
Solución
Respuesta (Indefinida)
[src]
// I*t I*t 2 I*t I*t 2 I*t \
|| cos(t)*e t*e *sin(t) t *cos(t)*e I*t*cos(t)*e I*t *e *sin(t) |
|| ----------- + ------------- + -------------- - --------------- - ---------------- for s = -I|
|| 4 4 4 4 4 |
/ || |
| || -I*t -I*t 2 -I*t -I*t 2 -I*t |
| -s*t || cos(t)*e t*e *sin(t) t *cos(t)*e I*t*cos(t)*e I*t *e *sin(t) |
| t*cos(t)*E dt = C + |< ------------ + -------------- + --------------- + ---------------- + ----------------- for s = I |
| || 4 4 4 4 4 |
/ || |
|| 2 2 3 |
|| cos(t) t*sin(t) s *cos(t) 2*s*sin(t) t*s *sin(t) s*t*cos(t) t*s *cos(t) |
||-------------------------- + -------------------------- - -------------------------- + -------------------------- + -------------------------- - -------------------------- - -------------------------- otherwise |
|| 4 s*t 2 s*t s*t 4 s*t 2 s*t s*t 4 s*t 2 s*t s*t 4 s*t 2 s*t s*t 4 s*t 2 s*t s*t 4 s*t 2 s*t s*t 4 s*t 2 s*t s*t |
\\s *e + 2*s *e + e s *e + 2*s *e + e s *e + 2*s *e + e s *e + 2*s *e + e s *e + 2*s *e + e s *e + 2*s *e + e s *e + 2*s *e + e /
∫e−sttcos(t)dt=C+⎩⎨⎧−4it2eitsin(t)+4t2eitcos(t)+4teitsin(t)−4iteitcos(t)+4eitcos(t)4it2e−itsin(t)+4t2e−itcos(t)+4te−itsin(t)+4ite−itcos(t)+4e−itcos(t)−s4est+2s2est+ests3tcos(t)+s4est+2s2est+ests2tsin(t)−s4est+2s2est+ests2cos(t)−s4est+2s2est+eststcos(t)+s4est+2s2est+est2ssin(t)+s4est+2s2est+esttsin(t)+s4est+2s2est+estcos(t)fors=−ifors=iotherwise
/ / 2\
| 2*\1 - s /
|-------------------- for 2*|arg(s)| < pi
|/ 2\ / 2\
|\1 + s /*\-2 - 2*s /
|
| oo
< /
| |
| | -s*t
| | t*cos(t)*e dt otherwise
| |
|/
|0
\
⎩⎨⎧(−2s2−2)(s2+1)2(1−s2)0∫∞te−stcos(t)dtfor2∣arg(s)∣<πotherwise
=
/ / 2\
| 2*\1 - s /
|-------------------- for 2*|arg(s)| < pi
|/ 2\ / 2\
|\1 + s /*\-2 - 2*s /
|
| oo
< /
| |
| | -s*t
| | t*cos(t)*e dt otherwise
| |
|/
|0
\
⎩⎨⎧(−2s2−2)(s2+1)2(1−s2)0∫∞te−stcos(t)dtfor2∣arg(s)∣<πotherwise
Piecewise((2*(1 - s^2)/((1 + s^2)*(-2 - 2*s^2)), 2*Abs(arg(s)) < pi), (Integral(t*cos(t)*exp(-s*t), (t, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.