Sr Examen
Integral de ch^2(3x) dx
Solución
Ha introducido
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1 / | | 2 | cosh (3*x) dx | / 0
$$\int\limits_{0}^{1} \cosh^{2}{\left(3 x \right)}\, dx$$
Integral(cosh(3*x)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 2 | 2 x*cosh (3*x) x*sinh (3*x) cosh(3*x)*sinh(3*x) | cosh (3*x) dx = C + ------------ - ------------ + ------------------- | 2 2 6 /
$$\int \cosh^{2}{\left(3 x \right)}\, dx = C - \frac{x \sinh^{2}{\left(3 x \right)}}{2} + \frac{x \cosh^{2}{\left(3 x \right)}}{2} + \frac{\sinh{\left(3 x \right)} \cosh{\left(3 x \right)}}{6}$$
Gráfica
Respuesta
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2 2 cosh (3) sinh (3) cosh(3)*sinh(3) -------- - -------- + --------------- 2 2 6
$$- \frac{\sinh^{2}{\left(3 \right)}}{2} + \frac{\sinh{\left(3 \right)} \cosh{\left(3 \right)}}{6} + \frac{\cosh^{2}{\left(3 \right)}}{2}$$
=
=
2 2 cosh (3) sinh (3) cosh(3)*sinh(3) -------- - -------- + --------------- 2 2 6
$$- \frac{\sinh^{2}{\left(3 \right)}}{2} + \frac{\sinh{\left(3 \right)} \cosh{\left(3 \right)}}{6} + \frac{\cosh^{2}{\left(3 \right)}}{2}$$
cosh(3)^2/2 - sinh(3)^2/2 + cosh(3)*sinh(3)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.