Question

Evaluate the following integration w.r.t. $x$
$\int \frac{1}{(4x+5{)}^2+1}dx$

Answer 1

According to question,

$\int \frac{1}{(4x+5{)}^2+1}dx$

Let $4x+5=t$

$⟹4dx=dt$

Hence,

$\frac{1}{4}\int \frac{1}{(t{)}^2+1}dx$

$⟹\frac{1}{4}ta{n}^{-1}t+C$

$⟹\frac{1}{4}ta{n}^{-1}(4x+5)+C$