Sr Examen
Integral de sh(x)^2ch(x)^2 dx
Solución
Ha introducido
[src]
1 / | | 2 2 | sinh (x)*cosh (x) dx | / 0
$$\int\limits_{0}^{1} \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}\, dx$$
Integral(sinh(x)^2*cosh(x)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 4 4 3 3 2 2 | 2 2 x*cosh (x) x*sinh (x) cosh (x)*sinh(x) sinh (x)*cosh(x) x*cosh (x)*sinh (x) | sinh (x)*cosh (x) dx = C - ---------- - ---------- + ---------------- + ---------------- + ------------------- | 8 8 8 8 4 /
$$\int \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}\, dx = C - \frac{x \sinh^{4}{\left(x \right)}}{8} + \frac{x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{4} - \frac{x \cosh^{4}{\left(x \right)}}{8} + \frac{\sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{8} + \frac{\sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{8}$$
Gráfica
Respuesta
[src]
4 4 2 2 3 3
cosh (1) sinh (1) cosh (1)*sinh (1) cosh (1)*sinh(1) sinh (1)*cosh(1)
- -------- - -------- + ----------------- + ---------------- + ----------------
8 8 4 8 8
$$- \frac{\cosh^{4}{\left(1 \right)}}{8} - \frac{\sinh^{4}{\left(1 \right)}}{8} + \frac{\sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{\sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{\sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4}$$
=
=
4 4 2 2 3 3
cosh (1) sinh (1) cosh (1)*sinh (1) cosh (1)*sinh(1) sinh (1)*cosh(1)
- -------- - -------- + ----------------- + ---------------- + ----------------
8 8 4 8 8
$$- \frac{\cosh^{4}{\left(1 \right)}}{8} - \frac{\sinh^{4}{\left(1 \right)}}{8} + \frac{\sinh^{3}{\left(1 \right)} \cosh{\left(1 \right)}}{8} + \frac{\sinh{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{8} + \frac{\sinh^{2}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{4}$$
-cosh(1)^4/8 - sinh(1)^4/8 + cosh(1)^2*sinh(1)^2/4 + cosh(1)^3*sinh(1)/8 + sinh(1)^3*cosh(1)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.