If $\int\frac{\sin^2x}{1+\sin^2x}dx=x-k\tan^{-1}(M\tan x)+C$, then;

$M=\frac{1}{\sqrt{2}}$ $K=\frac{1}{\sqrt{2}}$ $M=\frac{-1}{\sqrt{2}}$ $K=\frac{-1}{\sqrt{2}}$

$K=\frac{1}{\sqrt{2}}$

$I=\int\frac{\sin^2x}{1+\sin^2x}dx=\int(1-\frac{1}{1+\sin^2x})dx=\int(1-\frac{\sec^2x}{1+2\tan^2x})dx=x-\frac{1}{\sqrt{2}}\tan^{-1}(\sqrt{2}\tan x) + C$