Mathematics

Find :
$$\int { 2{ sin }^{ 3 } } \left( { x }\right) cos\left( { x }\right) dx$$


SOLUTION
$$\displaystyle\int{2{\sin}^{3}{x}\cos{x}dx}$$
$$=2\displaystyle\int{{\sin}^{3}{x}\cos{x}dx}$$
Let $$t=\sin{x}\Rightarrow dt=\cos{x}dx$$
$$=2\displaystyle\int{{t}^{3}dt}$$
$$=2\left[\dfrac{{t}^{4}}{4}\right]+c$$ where $$c$$ is the constant of integration.
$$=\left[\dfrac{{\sin}^{4}{x}}{2}\right]+c$$ where $$t=\sin{x}$$

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Subjective Medium Published on 17th 09, 2020
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