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
/
$$\int \sinh^{4}{\left(x \right)}\, dx = C + \frac{3 x \sinh^{4}{\left(x \right)}}{8} - \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} + \frac{3 x \cosh^{4}{\left(x \right)}}{8} + \frac{5 \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} - \frac{3 \sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}$$
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
$$- \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} - \frac{3 \sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{3 \sinh^{4}{\left(1 \right)}}{8} + \frac{5 \sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{3 \cosh^{4}{\left(1 \right)}}{8}$$
=
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
$$- \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4} - \frac{3 \sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{3 \sinh^{4}{\left(1 \right)}}{8} + \frac{5 \sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{3 \cosh^{4}{\left(1 \right)}}{8}$$
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.