Here are two problems that I tried but it seems I can not solve them. Thank you a lot for any help!

Problem 1: I need to evaluate the integral

$\displaystyle

\int {sinh^4xdx}

$

I know I need to use an identity. I tried rewriting it in this form:

$\displaystyle

\int {[sinh^2x]^2dx}

$

and use the following identity:

$\displaystyle

sinh^2x = \frac {1}{2}(cosh2x - 1)

$

but I can not seem to reach a solution.

Problem 2: Suppose that A and B are constants. Show that the function x(t)=Acoshkt+Bsinhkt is a solution of the differential equation

$\displaystyle

\frac {d^2x}{dt^2}={k^2}x(t)

$

Thank you!