Evaluate the intergal

Evaluate the intergal

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\[\int\limits_{}^{}3\sin^2(t)\cos^4(t)dt\]

My work: \[3\int\limits_{}^{}\sin^2(x)\cos^4(t)dt\] \[3\int\limits_{}^{}\sin^2(t)\cos^2(t)\cos^2(t)dt\] \[3\int\limits_{}^{}\frac{ 1 }{ 2 }(1-\cos(2t))(\frac{ 1 }{ 2 }(1+\cos(2t)))^2dt\] \[\frac{ 3 }{ 8 }\int\limits_{}^{}(1-\cos(2t))((1+\cos(2t)))^2dx\] \[\frac{ -3 }{ 8 }\int\limits_{}^{}((\cos^3(2t)+\cos^2(2t)+\cos(2t)+1) dt\] \[\frac{ -3 }{ 8 }\int\limits_{}^{}((cos^2(2t))(cos(2t))+\cos^2(2t)+\cos(2t)+1))dt\] \[\frac{ -3 }{ 8 }\int\limits_{}^{}(\cos^3(2t)+\cos^2(2t)+\cos(2t)+1)dt\]

I don't know what to do after :( .

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