How to integrate $\frac{2x+5}{x-1}$

Question

I want to know how to integrate a fraction where top and bottom are of the linear form $ax+b$, such as $\frac{2x+5}{x-1}$.

I know to do integration where we have linear form at the top and polynomial degree at the bottom.

Thanks

Answer 1

HINT

Use that

$$\frac{2x+5}{x-1}=\frac{2x-2+7}{x-1}=\frac{2(x-1)}{x-1}+\frac{7}{x-1}=2+\frac{7}{x-1}$$