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