Mathematics

$$\int x ^ { 2 } \cdot \cos \left( x ^ { 3 } \right) \sqrt { \sin ^ { 7 } \left( x ^ { 3 } \right) } \cdot d x$$


SOLUTION
$$\\Let\>sin(x^3)=t\\then\>\>cosx^3\times\>3x^2\>dx=dt\\or\>x^2cos(x^3)dx=(\frac{dt}{3})\\\therefore\>I=(\frac{1}{3})\int\sqrt{t^7}dt\\=(\frac{1}{3})\int{t^{(\frac{7}{2})}}dt\\=(\frac{1}{3})\times(\frac{t^{(\frac{9}{2})}}{(\frac{9}{2})})+C\\=(\frac{2}{27})\sqrt[9]{sin(x^3)}+C$$
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Subjective Medium Published on 17th 09, 2020
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