Question

Evaluate : $\int \frac{2x+2}{2x^2+4x-3}dx$

Answer 1

let $2x^2+4x-3=t$

differentiating both the sides with respect to x

(4x+4)dx=dt

2(2x+2)dx=dt

(2x+2)dx=dt/2

Upon substitution,

$\begin{array}{c}\int \frac{dt}{2t}=\frac{1}{2}\ln t\\ =\frac{1}{2}\ln \left(2x^2+4x-3\right)\end{array}$