Question

Integrate the function: $\frac {1}{\sqrt {1+4x^2}}$

Answer 1

$Let\ 2x = t$

$∴ 2dx = dt$

$⇒ ∫\frac {1}{\sqrt {1+4x^2}} dx$= $\frac 12∫\frac {dt}{\sqrt {1+t^2}}$

=$\frac 12[log\ |t+\sqrt {t_2+1}|]+C$ $[∫\frac {1}{\sqrt {x^2+a^2}}dt = log\ |x+\sqrt {x^2+a^2}|]$

=$\frac 12 \ log\ |2x+\sqrt {4x^2+1}|+C$