Question

Evaluate
$\int \frac{x+2}{2X^2+6x+5}dx$

Answer 1

$I=\int \frac{x+2}{2x^2+6x+5}$

derivative of denominator $\frac{d}{dt}(2x^2+6c+5)=4x+6$

$\therefore$ arranging in the single form we can write

$=\frac{1}{4}\int \frac{4x+8}{2x^2+6x+5}dx$

$=\frac{1}{4}\int \frac{4x+6+2}{2x^2+6x+5}dx$

$=\frac{1}{4}\int \frac{4x+6}{2x^2+6x+5}+\frac{1}{4}\int \frac{2}{2x^2+6x+5}dx$.