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Evaluate the integral.
$ \displaystyle \int \sin^2 x \cos^3 x dx $
$ \displaystyle \int \sin^3 \theta \cos^4 \theta d \theta $
$ \displaystyle \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^5 \theta d \theta $
$ \displaystyle \int_0^{\frac{\pi}{2}} \sin^5 x dx $
$ \displaystyle \int \sin^5 (2t) \cos^2 (2t) dt $
$ \displaystyle \int t \cos^5 (t^2) dt $
