Mathematics

Write a value of 
$$\int { \cos ^{ 4 }{ x }  } \sin { x } dx$$


SOLUTION
Let $$t=\cos{x}\Rightarrow\,dt=-\sin{x}dx$$

$$I=\displaystyle\int{{\cos}^{4}{x}\sin{x}dx}$$

$$=\displaystyle\int{-{t}^{4}dt}$$

$$=\dfrac{-{t}^{5}}{5}+c$$    ......where $$c$$ is the constant of integration.

$$=-\dfrac{{\cos}^{5}{x}}{5}+c$$    .....where $$t=\cos{x}$$
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Subjective Medium Published on 17th 09, 2020
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