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

The integral of cos^2(x)x 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 cos^2(x)x

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

Solution steps

\int cos^{2} (x) 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

(\frac{1}{x}), 2

\frac{1}{s ^{2} ( s ^{2} + 4 )}

y = 3 x - 6, (2, 4)

\frac{d}{d x} (\frac{2 x ^{3} - 5 x ^{2} + 4 x}{( x - 1 ) ^{2}})

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