Question

Integrate the function: $\frac {sec^2x}{\sqrt {tan^2 x+4}}$

Answer 1

$Let\ tan\ x = t$

$∴ sec^2x\ dx = dt$

$⇒ ∫\frac {sec^2x}{\sqrt {tan^2 x+4}}\ dx = ∫\frac {dt}{\sqrt {t^2+2^2}}$

$=log\ |t+\sqrt {t^2+4}|+C$

$=log\ |tan x+\sqrt {tan^2 x+4}|+C$