Integrate the following function with respect to $x$
$x^{2} . cos (x^{3}) \sqrt{{sin}^{7} (x^{3})}$

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Solution

$= \int x^{e} cos x^{3} \sqrt{sin (x^{3})}$
$sin (x^{3}) = t$
$(3 x^{2}) cos (x^{3}) = d t / d x$
$= \frac{1}{3} \int (t)^{7 / 2} \Rightarrow \frac{12}{3 (9)} t^{9 / 2}$
$= \frac{2}{27} ({sin}^{9 / 2} (x)^{3})$

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