A definite integral that does not depend on the scale

In this question, \(a\) is a positive constant.

1. Express \(\dfrac{3x+5a}{(x+a)(x+3a)}\) in partial fractions.[2]
2. Hence show that \(\displaystyle\int_0^{a}\dfrac{3x+5a}{(x+a)(x+3a)}\,\mathrm dx=\ln\dfrac{32}{9}\).[3]
3. Explain why the value in (b) does not depend on \(a\), and use the same idea to write down \(\displaystyle\int_0^{2a}\dfrac{3x+5a}{(x+a)(x+3a)}\,\mathrm dx\) in the form \(\ln k\).[3]