Final answer to the problem
$-\ln\left|\mathrm{tanh}\left(\frac{1}{2x}\right)\right|+\frac{-u}{\mathrm{cosh}\left(u\right)}+C_0$
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Step-by-step Solution
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1
Simplify the expression
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$\int\frac{1}{x^2\mathrm{sinh}\left(\frac{1}{x}\right)}dx+\int\frac{1}{x^2\mathrm{cosh}\left(\frac{1}{x}\right)}dx$
Learn how to solve problems step by step online. Find the integral int((1/x)^21/sinh(1/x)+(1/x)^21/cosh(1/x))dx. Simplify the expression. The integral \int\frac{1}{x^2\mathrm{sinh}\left(\frac{1}{x}\right)}dx results in: -\ln\left(\mathrm{tanh}\left(\frac{1}{2x}\right)\right). The integral \int\frac{1}{x^2\mathrm{cosh}\left(\frac{1}{x}\right)}dx results in: -\int\frac{1}{\mathrm{cosh}\left(u\right)}du. Gather the results of all integrals.
Final answer to the problem
$-\ln\left|\mathrm{tanh}\left(\frac{1}{2x}\right)\right|+\frac{-u}{\mathrm{cosh}\left(u\right)}+C_0$
