Question

the integration of (e^x)/(1-E^2x)^3/2 with respect to x

We are currently doing integration by tables, but I can't find the formula that I should use!

Answer 1

Wolfram says:

http://integrals.wolfram.com/index.jsp?expr=e%5Ex%2F%281+-+e%5E%282x%29%29%5E%283%2F2%29&random=false

Answer 2

If u = e^x, then

(e^x)/(1-e^2x)^3/2 dx
= du/(1-u^2)^3/2

Now you can easily find that the integral is

u/√(1-u^2)

which is what Reiny provided.