Evaluate the integral using subsitution rule $\int {cos}^{3} x sin x d x$ $int cos^3xsinx dx$ ?

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Answer 1 · 2017-01-19T01:54:30

$\int {cos}^{3} (x) sin (x) d x = \frac{- {cos}^{4} (x)}{4} + C$ $intcos^(3)(x)sin(x)dx=(-cos^(4)(x))/4+C$

Let

$u = cos (x)$ $u=cos(x)$

then

$d u = - sin (x)$ $du=-sin(x)$

Then we can write

$\int {cos}^{3} (x) sin (x) d x = - \int u^{3} d u = - \frac{u^{4}}{4} + C$ $intcos^(3)(x)sin(x)dx=-intu^3du=-u^(4)/4+C$

Then by substituting $cos (x)$ $cos(x)$ back in we get

$ul(intcos^(3)(x)sin(x)dx=(-cos^(4)(x))/4+C)$

Evaluate the integral using subsitution rule int cos^3xsinx dx∫cos3xsinxdxint cos^3xsinx dx?