Question

Integration of cosx ​dx/(10 + sin2x)

Answer 1

$t=sinx\\\\ \int {\frac{cos\ x}{10+sin^2x}} \ dx \\\\=\int {\frac{1}{10+t^2}} \ dt\\\\=\frac{1}{\sqrt{10}}tan^{-1}(\frac{t}{\sqrt{10}})\\\\=\frac{1}{\sqrt{10}}tan^{-1}(\frac{sin\ x}{\sqrt{10}})$