`int sinh^2(x) cosh(x) dx` Evaluate the indefinite integral.

You need to evaluate the indefinite integral by using the substitution `sinh x = t` , such that:

`sinh x = t =>cosh x dx = dt `

`int sinh^2 x*cosh x dx = int t^2 dt`

Using the formula `int t^n dt = (t^(n+1))/(n+1)` yields:

`int t^2 dt = t^3/3 + c`

Replacing back `sinh x` for t yields:

`int sinh^2 x*cosh x dx = (sinh^3 x)/3 + c`

Hence, evaluating the indefinite integral, yields `int sinh^2 x*cosh x dx = (sinh^3 x)/3 + c.`