Integration by partial fractions

[Geocentric]

Homework Statement

I am stuck on this integral.
1) (a - bx)/(a^2 + b^2 - 2abx)^(3/2)
I tried some substitutions but end up with complicated expressions. How to decompose into partial fractions when the denominator is raised to fractional powers? Can anyone please help me out?

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

I am stuck on this integral.
1) (a - bx)/(a^2 + b^2 - 2abx)^(3/2)
I tried some substitutions but end up with complicated expressions. How to decompose into partial fractions when the denominator is raised to fractional powers? Can anyone please help me out?

There is no point to using partial fractions in this problem. I would split this into two integrals like so:
$$a \int \frac{dx}{(a^2 + b^2 - 2abx)^{3/2}} -~b~ \int \frac{x dx}{(a^2 + b^2 - 2abx)^{3/2}}$$

The first integral can definitely be done with an ordinary substitution. I haven't worked through the second integral, but I think it can also be done with an ordinary substitution, maybe the same one.