Question

Solve $\int x^2.\cos \left(x^3\right)\sqrt{{\sin }^7\left(x^3\right)}dx$

Answer 1

Put $x^3=t$

$3x^2=dt$

$=\frac{1}{3}\int cost\sqrt{si{n}^{7}t}dt$

put $sint=y$

$costdt=-dy$

$=-\frac{1}{3}\int \sqrt{y^7}dy$

$=-\frac{2}{27}{y}^{\frac{9}{2}}+C=-\frac{2}{27}si{n}^{\frac{9}{2}}t+C$

$=\frac{-2}{27}(sin{x}^3{)}^{\frac{9}{2}}+C$