What is the integral of 2y-x^2e^{-y} ?

The integral of 2y-x^2e^{-y} is y^2+x^2e^{-y}+C

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integral of 2y-x^2e^{-y}

\int 2 y - x^{2} e^{- y} d y

y^{2} + x^{2} e^{- y} + C

Solution steps

\int 2 y - x^{2} e^{- y} 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 y d y - \int x^{2} e^{- y} d y

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

\int x^{2} e^{- y} d y = - x^{2} e^{- y}

= y^{2} - (- x^{2} e^{- y})

Simplify

= y^{2} + x^{2} e^{- y}

Add a constant to the solution

= y^{2} + x^{2} e^{- y} + C

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What is the integral of 2y-x^2e^{-y} ?
The integral of 2y-x^2e^{-y} is y^2+x^2e^{-y}+C