I don't understandhow (1/(1-sinx^2)^3/2 )cosx dx

goes to (1/cosx^2 ) dx

Hello

Because 1-sin^{2}x=cos^{2}x

That gives you:

\frac{cosx}{(cos^{2}x)^{\frac{3}{2}}}=\frac{cosx}{ cos^{3}x}=\frac{1}{cos^{2}x}=sec^{2}x

Thank you