Question

Evaluate the integral of sin2x dx/(2+sin² x)

Answer 1

Ans:-

$\int\dfrac{Sin2x}{2+sin^2x}dx$

$Sin2x=2\times(Sinx)\times(Cosx)$

put $2+Sin^2x=t \Rightarrow 2Sinxcosxdx=dt$

$\int\dfrac{dt}{t}=lnt +C$

$\Rightarrow ln(2+Sin^2x)+C$