Integral de sinh^4x dx
Solución
Respuesta (Indefinida)
[src]
/
| 3 4 4 3 2 2
| 4 3*cosh (x)*sinh(x) 3*x*cosh (x) 3*x*sinh (x) 5*sinh (x)*cosh(x) 3*x*cosh (x)*sinh (x)
| sinh (x) dx = C - ------------------ + ------------ + ------------ + ------------------ - ---------------------
| 8 8 8 8 4
/
∫sinh4(x)dx=C+83xsinh4(x)−43xsinh2(x)cosh2(x)+83xcosh4(x)+85sinh3(x)cosh(x)−83sinh(x)cosh3(x)
Gráfica
4 4 2 2 3 3
3*cosh (1) 3*sinh (1) 3*cosh (1)*sinh (1) 3*cosh (1)*sinh(1) 5*sinh (1)*cosh(1)
---------- + ---------- - ------------------- - ------------------ + ------------------
8 8 4 8 8
−43sinh2(1)cosh2(1)−83sinh(1)cosh3(1)+83sinh4(1)+85sinh3(1)cosh(1)+83cosh4(1)
=
4 4 2 2 3 3
3*cosh (1) 3*sinh (1) 3*cosh (1)*sinh (1) 3*cosh (1)*sinh(1) 5*sinh (1)*cosh(1)
---------- + ---------- - ------------------- - ------------------ + ------------------
8 8 4 8 8
−43sinh2(1)cosh2(1)−83sinh(1)cosh3(1)+83sinh4(1)+85sinh3(1)cosh(1)+83cosh4(1)
3*cosh(1)^4/8 + 3*sinh(1)^4/8 - 3*cosh(1)^2*sinh(1)^2/4 - 3*cosh(1)^3*sinh(1)/8 + 5*sinh(1)^3*cosh(1)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.