What is the integral of 2ysin(y) ?

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

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integral of 2ysin(y)

\int 2 y sin (y) d y

2 (- y cos (y) + sin (y)) + C

Solution steps

\int 2 y sin (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int y sin (y) d y

Apply Integration By Parts

: - y cos (y) - \int - cos (y) d y

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

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

= 2 (- y cos (y) - (- sin (y)))

Simplify

= 2 (- y cos (y) + sin (y))

Add a constant to the solution

= 2 (- y cos (y) + sin (y)) + C

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