What is the integral of (-3xy^2-2ycos(x)) ?

The integral of (-3xy^2-2ycos(x)) is -y^2cos(x)-xy^3+C

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integral of (-3xy^2-2ycos(x))

\int (- 3 x y^{2} - 2 y cos (x)) d y

- y^{2} cos (x) - x y^{3} + C

Solution steps

\int - 3 x y^{2} - 2 y cos (x) 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 2 cos (x) y d y - \int 3 x y^{2} d y

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

\int 3 x y^{2} d y = x y^{3}

= - y^{2} cos (x) - x y^{3}

Add a constant to the solution

= - y^{2} cos (x) - x y^{3} + C

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What is the integral of (-3xy^2-2ycos(x)) ?
The integral of (-3xy^2-2ycos(x)) is -y^2cos(x)-xy^3+C