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

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

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integral of y^2*cos(y)

\int y^{2} \cdot 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{5}{2 x - 2} d x

(1 + x^{6}) \frac{d y}{d x} = \frac{x ^{5}}{y}

\int_{0}^{4} \frac{e ^{x}}{x} d x

x \to 1 + lim (\frac{x}{ln ( x )})

x \to 3 lim (x^{2} + x - 5)

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