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Popular Calculus >

integral of x+e^{-y}

Solution

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

Solution

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

Solution steps

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

Apply the Sum Rule:

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

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

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

\int x d x = \frac{x ^{2}}{2}

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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