Question

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Answer 1

\[\int\limits \cos^{2}xsin^{2}xdx => \int\limits\left(\frac{1+\cos2x}{2}\right) \left(\frac{1-\cos2x}{2}\right) dx\]
maybe or
\[\int\limits \cos^{2}xsin^{2}xdx => \int\limits(1-\sin^{2}x)(\sin^{2}x) dx\]

Answer 2

\[\int\limits(1-\sin^{2}x)(\sin^{2}x) dx => \int\limits \sin^{2}x-\sin ^{4} xdx \]

Answer 3

\[=> \int\limits \sin^{2}x dx-\int\limits \sin^{4}xdx \]

Answer 4

you may wanna do it like this rather i guess..

sin^2x cos^2x = sin^2 (2x) / 4