A difficult question (for me)

[13olt3]

[IMG]http://img258.imageshack.us/img258/6277/mathsim9.th.jpg[/img]

This question is right out of a text book, i'm fairly new here so if i happen to be breaking any rules then please delete this post.
I've tried to do it myself and cant come of with the answer that they provide in part (c) any insight or inspiration?

[Ahmad]

Looks like they tried to hide a Hyperbolic function question, in any case, I suggest you try a substitution along the lines of or , then turn the integral into one of a rational function (of polynomials) and finally using the method of partial fractions.

[bigtick]

Just let u=e^(2x)-e^(-2x), the integrand becomes 1/(2u).

[Ahmad]

Yup, that's even simpler. Whenever you see just exponentials think of making an exponential substitution, the systematic one will always work (if you don't spot anything easier).

Another way:

[AppleXY]

Yup, that's even simpler.

Another way:

Wow. I like that

[13olt3]

Thanks guys know this is a late reply but this helps a lot! ^^b