Integral help

[Ewan]

Well, I should probably know this, but in my cramming for an exam, I just can't do this integral:

dT/(F^4 + T^4)

F is a constant.

I know it's a substitution integration, but I just can't get my head around it, it's been too long since I had to do this stuff properly.

The method/substitution itself is what I am after, it's a "show that blaa = blaa" question so I know if I've done it right.


FYI, the answer should be:

ln(1+z/1-z) + arctan(z) + C
where z = T/F (< 1) and C = const. of integration.

[Troll King]

Have you tried using the form:

Int: du/(a^2+u^2) = (1/a)arctan(u/a) + C

With T to the exponent 4, there'll be a bit more work to do, but it's a start.

[Ewan]

Meh, fuck it, the exam's in an hour. Probably won't need it anyway; I can choose which questions to do in that section, and can do one of the probable ones quite well.

Thanks for helping though TK.