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

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

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integral of y^2cos(y)

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

y^{2} sin (y) - 2 (- y cos (y) + sin (y)) + C

Solution steps

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

Apply Integration By Parts

: y^{2} sin (y) - \int 2 y sin (y) d y

= y^{2} sin (y) - \int 2 y sin (y) d y

\int 2 y sin (y) d y = 2 (- y cos (y) + sin (y))

= y^{2} sin (y) - 2 (- y cos (y) + sin (y))

Add a constant to the solution

= y^{2} sin (y) - 2 (- y cos (y) + sin (y)) + C

\int \frac{x + 4}{x - 1} d x

\int \frac{( cos ( 3 x ) ) ^{5}}{csc ( 3 x )} d x

\int \frac{sin ^{3} ( x )}{sec ( x )} d x

\int 2 x (1 - x^{2}) d x

\int 3 x e^{- 4 x^{2}} d x

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