Mathematics

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


SOLUTION
$$=\displaystyle \int x^e \cos x^3 \sqrt {\sin (x^3)}$$
$$\sin (x^3)=t$$
$$(3x^2) \cos (x^3)=dt /dx$$
$$=\dfrac {1}{3} \displaystyle \int (t)^{7/2} \ \Rightarrow \ \dfrac {12}{3(9)}t^{9/2}$$
$$=\dfrac {2}{27}(\sin ^{9/2}(x)^3)$$

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Subjective Medium Published on 17th 09, 2020
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