$\int\frac{1}{(x+5)\sqrt{x+4}}dx$ is:
Answer & explanation
Correct answer: option 2
$I=\int\frac{1}{(x+5)\sqrt{x+4}}dx$. Put $x + 4 = t^2$ to get $dx = 2t\, dt$
$⇒I=\int\frac{2t\,dt}{(t^2+1)t}=2\int\frac{dt}{t^2+1}=2tan^{-1}(t)+c=2tan^{-1}(\sqrt{x+4})+c$