What is the integral of xcosh(ax) ?

The integral of xcosh(ax) is 1/a xsinh(ax)-1/(a^2)cosh(ax)+C

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integral of xcosh(ax)

\int x cosh (a x) d x

\frac{1}{a} x sinh (a x) - \frac{1}{a ^{2}} cosh (a x) + C

Solution steps

\int x cosh (a x) d x

Apply Integration By Parts

: \frac{1}{a} x sinh (a x) - \int \frac{1}{a} sinh (a x) d x

= \frac{1}{a} x sinh (a x) - \int \frac{1}{a} sinh (a x) d x

\int \frac{1}{a} sinh (a x) d x = \frac{1}{a ^{2}} cosh (a x)

= \frac{1}{a} x sinh (a x) - \frac{1}{a ^{2}} cosh (a x)

Add a constant to the solution

= \frac{1}{a} x sinh (a x) - \frac{1}{a ^{2}} cosh (a x) + C

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What is the integral of xcosh(ax) ?
The integral of xcosh(ax) is 1/a xsinh(ax)-1/(a^2)cosh(ax)+C