Question

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

Answer 1

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

$4x+5=t$

$4dx=dt$

$dx=\frac{dt}{4}$

$\frac{1}{4}\int \frac{dt}{t^2+1}=\frac{1}{4}{tan}^{-1}\left(t\right)+c$

$=\frac{1}{4}{tan}^{-1}(4x+5)+c$