Question

integrate (e^t + e^-t)²

Answer 1

The first step is just to expand the polynomial:

e^2t + 2 + e^-2t

Now integrate each term.

Or, remember that your function is just

(2 cosh t)^2 = 4cosh^2(t)
now use the half-angle formula for hyperbolic functions, and you will get the same answer.

Hmm. I guess just expanding the polynomial above is less work...