∫√(1-x^2 ) dx

Letting x = sin θ,

dx/dθ = cos θ

∫√(1-x^2 ) dx

=∫√(1-sin^2θ ) cos θ dθ

=∫cos^2 θ dθ

=∫ (1-sin^2θ) dθ

=θ -2sinθ(-cosθ) + c

=θ +2sinθcosθ + c

=sin^(-1)θ + 2x√(1-x^2 ) + c

Is this correct? Please help me to check whether it is correct or not, and point out my mistake, if any. Thank you.