Question

Integrate sin^2(x)cos^2(x)

Answer 1

\[\int\limits_{}^{}\sin^2xcos^2xdx\]

Answer 2

Hint: \[ \sin^2 x + \cos^2 x = 1 \]would help. You can get the integrand in terms of sine, only and then use Integration by Parts to complete. Hope that helped! :)

Answer 3

Hmm this is what I have so far, using half angle formula I get\[\frac{ 1 }{ 4 }\int\limits_{}^{}(1-\cos2x)(1-\sin2x)dx\]\[\frac{ 1 }{ 4 }\int\limits_{}^{}(1-\sin2x-\cos2x+\sin2xcos2x)\]\[\frac{ 1 }{ 4 }x + \frac{ 1 }{ 8 }\cos2x-\frac{ 1 }{ 8 }\sin2x+\frac{ 1 }{ 4 }\sin^22x +c\]Anybody have any input?