Integrate sinh^2x dx?

Question

Can anyone do it?

Answer 1

Integrate ∫sinh²x dx.

Remember the identities.

2sinh²x = cosh(2x) - 1
sinh(2x) = 2(sinh x)(cosh x)

∫sinh²x dx = ½∫(cosh(2x) - 1)dx = ½(½sinh(2x) - x) + C
= ½{(sinh x)(cosh x) - x} + C