Question

Evaluate
${\int }_0^2\frac{6x+3}{x^2+4}dx$

Answer 1

$I=\int \frac{6x+3}{x^2+4}dx$

$I=\int \frac{6x}{x^2+4}dx+\int \frac{3}{x^2+4}dx$

$I=3\int \frac{2x}{x^2+4}dx+\int \frac{3}{x^2+2^2}dx$

$I=3\log |x^2+4|+\frac{3}{2}{\tan }^{-1}\frac{x}{2}+C$

Hence, this is the answer.