What is the integral of 2ysin(x)-4 ?

The integral of 2ysin(x)-4 is -4y+y^2sin(x)+C

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integral of 2ysin(x)-4

\int 2 y sin (x) - 4 d y

- 4 y + y^{2} sin (x) + C

Solution steps

\int 2 y sin (x) - 4 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 4 d y + \int 2 sin (x) y d y

\int 4 d y = 4 y

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

= - 4 y + y^{2} sin (x)

Add a constant to the solution

= - 4 y + y^{2} sin (x) + C

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What is the integral of 2ysin(x)-4 ?
The integral of 2ysin(x)-4 is -4y+y^2sin(x)+C