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