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

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

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integral of y^2sin(y)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

sin (2 x + 3)

x \to 0 lim (x^{3} cos (\frac{5}{x}))

\frac{\partial}{\partial y} (\frac{x}{y + 1})

y = 3 x^{2}, y = 2 - x, x = 0

\int \frac{4}{3 x} d x

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