Question

Solve $\int \frac{1}{\sqrt{x^2+4x+5}}dx$

Answer 1

Given that:

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

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

$=\int \frac{1}{\sqrt{(x+2{)}^2+1}}dx$

$=\ln \left[(x+2)+\sqrt{(x+2{)}^2+1}\right]$+constant