Thanks
I think you first need to get rid of that square root by doing some substitution.
Try . It might not actually work out...but that 4th power has to be removed before you can replace that with just .
At least that's what I would try. You just shouldn't use integration by parts if it looks like you can still substitute.
Okay, this will be a mess. It takes lots of substitutions, but having patience makes sense.
First rewrite your integral
Substitute the integral becomes
Make another substitution according to the integral becomes
Now a final substitution defined by (We're gettin' close.)
Now this is easy, so we have
After back substitute we finally-happily get that