Question

Integrate:
$\int \frac{x+2^x.\log 2}{x^2+2^{x+1}}dx$

Answer 1

$I=\int \frac{x+2^x.\log 2}{x^2+2^{x+1}}dx$

Let $u=x^2+2^{x+1}$

$\Rightarrow du=2x+2^{x+1}\log 2dx$

$=2(x+2^x\log 2)dx$

Substituting

$I=\int \frac{du}{2u}$$

$=\frac{1}{2}\log u+C$

$I=\frac{1}{2}\log (x^2+2^{x+1})+C$