What is the integral of x(cos(x))^2 ?

The integral of x(cos(x))^2 is 1/2 x(x+1/2 sin(2x))-1/2 ((x^2)/2-1/4 cos(2x))+C

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integral of x(cos(x))^2

integral

x (cos (x))^{2}

\frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x)) + C

Solution steps

\int x (cos (x))^{2} d x

Simplify

= \int x cos^{2} (x) d x

Apply Integration By Parts

: \frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \int \frac{1}{2} (x + \frac{1}{2} sin (2 x)) d x

= \frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \int \frac{1}{2} (x + \frac{1}{2} sin (2 x)) d x

\int \frac{1}{2} (x + \frac{1}{2} sin (2 x)) d x = \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x))

= \frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x))

Add a constant to the solution

= \frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x)) + C

x^{8} + 9

(9 x + 36)^{- 1}

\frac{y ^{3}}{x ^{4}}

\frac{1}{a ^{2} + x ^{2}}

\frac{1}{x ( 1 - x )}

What is the integral of x(cos(x))^2 ?
The integral of x(cos(x))^2 is 1/2 x(x+1/2 sin(2x))-1/2 ((x^2)/2-1/4 cos(2x))+C