Question

Find, using substitution, the integral of:
e^x /sqrt[e^(2x) -1] dx

Answer 1

let u = e^x
then u^2 = e^(2x)
and du/dx = e^x
dx = du/e^x = du/u

ʃ e^x /sqrt[e^(2x) -1] dx
= ʃ u/√(u^2 - 1) du/u
= ʃ 1/√(u^2 - 1) du

= ln (√(u^2 - 1) + u) , from my old integration formulas

= ln((√(e^(2x) - 1) + e^x) + C

Answer 2

I've just found that integration formula (which I'd forgotten about). No wonder I kept getting stuck! Thank you.