Sr Examen
Integral de sinh^4(x) dx
Solución
Ha introducido
[src]
1 / | | 4 | sinh (x) dx | / 0
$$\int\limits_{0}^{1} \sinh^{4}{\left(x \right)}\, dx$$
Integral(sinh(x)^4, (x, 0, 1))
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 /
$$\int \sinh^{4}{\left(x \right)}\, dx = C + \frac{3 x \sinh^{4}{\left(x \right)}}{8} - \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} + \frac{3 x \cosh^{4}{\left(x \right)}}{8} + \frac{5 \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} - \frac{3 \sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}$$
Gráfica
Respuesta
[src]
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.