Integral de sin^2x/cos^5x dx
Solución
Respuesta (Indefinida)
[src]
/
|
| 2 3
| sin (x) log(1 + sin(x)) log(-1 + sin(x)) sin (x) + sin(x)
| ------- dx = C - --------------- + ---------------- + --------------------------
| 5 16 16 2 4
| cos (x) 8 - 16*sin (x) + 8*sin (x)
|
/
∫cos5(x)sin2(x)dx=C+8sin4(x)−16sin2(x)+8sin3(x)+sin(x)+16log(sin(x)−1)−16log(sin(x)+1)
Gráfica
3
log(1 + sin(1)) log(1 - sin(1)) sin (1) + sin(1)
- --------------- + --------------- + --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
16log(1−sin(1))−16log(sin(1)+1)+−16sin2(1)+8sin4(1)+8sin3(1)+sin(1)
=
3
log(1 + sin(1)) log(1 - sin(1)) sin (1) + sin(1)
- --------------- + --------------- + --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
16log(1−sin(1))−16log(sin(1)+1)+−16sin2(1)+8sin4(1)+8sin3(1)+sin(1)
-log(1 + sin(1))/16 + log(1 - sin(1))/16 + (sin(1)^3 + sin(1))/(8 - 16*sin(1)^2 + 8*sin(1)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.