Need help with a horrible integral Dont get scared

[Bkkkk]

Need help with a horrible integral! Dont get scared

Homework Statement

Prove that

Homework Equations

Cosh²-Sinh²=1

The Attempt at a Solution

I have used the subsitution r=2GM/c²Cosh²(x) and the integral is simplified to:

4GM/c²*$$\int$$Cosh²(x)dx

Integrating was done in Mathematica but I can't do the simplification needed for the equation to look like the answer.

 

[Dick]

The integral of cosh(x)^2 is 2*cosh(x)*sinh(x)/4+x/2. The cosh(x)*sinh(x) is the first term in your answer, yes? The x/2 part is the hard one. You've got r~cosh(x)^2 (I'll ignore the constant factors). So x=arccosh(r^(1/2)). arccosh(a)=ln(a+sqrt(a^2-1)). Doesn't that look like the second term? You can throw away the third term. It's just a constant.