# Solve this algebraic integral

1. Jan 23, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
$\int \dfrac{x+2}{\sqrt{(x-2)(x-3)}} dx$

3. The attempt at a solution

I've tried substitutions like assuming (x-2) = t^2 or x= 1/t or x=1/t^2, but none of them seems to ease the problem. Breaking the integral into two helps to integrate the second but first integral still remains complicated. I'm also sure that trig substitutions won't work here.

2. Jan 23, 2014

### Tanya Sharma

Rewrite the given integral as $\frac{1}{2} \int \dfrac{2x-5}{\sqrt{x^2-5x+6}} dx$ + $\frac{9}{2}\int \dfrac{1}{\sqrt{(x-\frac{5}{2})^2-(\frac{1}{2})^2}} dx$

I hope the two integrals are easy to handle .