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Popular Calculus >

integral of (xe^x+e^x)

Solution

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

Solution

e^{x} x + C

Solution steps

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

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

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

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

Simplify

= e^{x} x

Add a constant to the solution

= e^{x} x + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (xe^x+e^x) ?
The integral of (xe^x+e^x) is e^xx+C