Integration Rational Functions

Question

Hi guys I am quite stuck on this question, would really appreciate some help. The finite region bounded by the curve with equation $y = \frac{2}{(x-1)(x-3)}$ and the lines $x = 4$ and $y = 1/4$ is denoted by $R$. Show that the area $R$ is $\ln (3/2) - 1/4$

Answer 1

HINT

Let $$ \frac{2}{(x-1)(x-3)} = \frac{A}{x-1} + \frac{B}{x-3} $$ and find the values of $A$ and $B$ for which this is true.

Then, $$ \int \frac{2dx}{(x-1)(x-3)} = A \int \frac{dx}{x-1} + B \int \frac{dx}{x-3} $$ and the RHS becomes a pair of natural logs...