What is the integral of ycos^2(y) ?

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

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integral of ycos^2(y)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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