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Popular >

integral of x-e^{-x}

Solution

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

Solution

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

Solution steps

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

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

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

= \frac{x ^{2}}{2} - (- e^{- x})

Simplify

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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