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Popular Calculus >

integral of (-e^x+x)

Solution

\int (- e^{x} + x) d x

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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