Integral de ((coshx)^4)*((sinhx)^2) dx
Solución
Respuesta (Indefinida)
[src]
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| 6 5 3 3 6 5 2 4 4 2
| 4 2 x*cosh (x) sinh (x)*cosh(x) cosh (x)*sinh (x) x*sinh (x) cosh (x)*sinh(x) 3*x*cosh (x)*sinh (x) 3*x*cosh (x)*sinh (x)
| cosh (x)*sinh (x) dx = C - ---------- - ---------------- + ----------------- + ---------- + ---------------- - --------------------- + ---------------------
| 16 16 6 16 16 16 16
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$$\int \sinh^{2}{\left(x \right)} \cosh^{4}{\left(x \right)}\, dx = C + \frac{x \sinh^{6}{\left(x \right)}}{16} - \frac{3 x \sinh^{4}{\left(x \right)} \cosh^{2}{\left(x \right)}}{16} + \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{4}{\left(x \right)}}{16} - \frac{x \cosh^{6}{\left(x \right)}}{16} - \frac{\sinh^{5}{\left(x \right)} \cosh{\left(x \right)}}{16} + \frac{\sinh^{3}{\left(x \right)} \cosh^{3}{\left(x \right)}}{6} + \frac{\sinh{\left(x \right)} \cosh^{5}{\left(x \right)}}{16}$$
6 6 2 4 5 3 3 5 4 2
cosh (1) sinh (1) 3*cosh (1)*sinh (1) sinh (1)*cosh(1) cosh (1)*sinh (1) cosh (1)*sinh(1) 3*cosh (1)*sinh (1)
- -------- + -------- - ------------------- - ---------------- + ----------------- + ---------------- + -------------------
16 16 16 16 6 16 16
$$- \frac{3 \sinh^{4}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{16} - \frac{\cosh^{6}{\left(1 \right)}}{16} - \frac{\sinh^{5}{\left(1 \right)} \cosh{\left(1 \right)}}{16} + \frac{\sinh^{6}{\left(1 \right)}}{16} + \frac{\sinh{\left(1 \right)} \cosh^{5}{\left(1 \right)}}{16} + \frac{\sinh^{3}{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{6} + \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{4}{\left(1 \right)}}{16}$$
=
6 6 2 4 5 3 3 5 4 2
cosh (1) sinh (1) 3*cosh (1)*sinh (1) sinh (1)*cosh(1) cosh (1)*sinh (1) cosh (1)*sinh(1) 3*cosh (1)*sinh (1)
- -------- + -------- - ------------------- - ---------------- + ----------------- + ---------------- + -------------------
16 16 16 16 6 16 16
$$- \frac{3 \sinh^{4}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{16} - \frac{\cosh^{6}{\left(1 \right)}}{16} - \frac{\sinh^{5}{\left(1 \right)} \cosh{\left(1 \right)}}{16} + \frac{\sinh^{6}{\left(1 \right)}}{16} + \frac{\sinh{\left(1 \right)} \cosh^{5}{\left(1 \right)}}{16} + \frac{\sinh^{3}{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{6} + \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{4}{\left(1 \right)}}{16}$$
-cosh(1)^6/16 + sinh(1)^6/16 - 3*cosh(1)^2*sinh(1)^4/16 - sinh(1)^5*cosh(1)/16 + cosh(1)^3*sinh(1)^3/6 + cosh(1)^5*sinh(1)/16 + 3*cosh(1)^4*sinh(1)^2/16
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.