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