Evaluate the indefinite and definite integrals.
(a) ∫ x 2 1 + x 3 d x {\displaystyle \int x^{2}{\sqrt {1+x^{3}}}~dx}
(b) ∫ π 4 π 2 cos ( x ) sin 2 ( x ) d x {\displaystyle \int _{\frac {\pi }{4}}^{\frac {\pi }{2}}{\frac {\cos(x)}{\sin ^{2}(x)}}~dx}
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