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Popular >

integral of (x+xe^x)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 0 of (x^2+1)^{1/x}

x \to 0 lim ((x^{2} + 1)^{\frac{1}{x}})

integral of 5x^4e^{9x^5}

\int 5 x^{4} e^{9 x^{5}} d x

derivative of 1/4 x^3+x-1

\frac{d}{d x} (\frac{1}{4} x^{3} + x - 1)

limit as x approaches 3 of 4x^2-2x+1

x \to 3 lim (4 x^{2} - 2 x + 1)

slope of (-5.1)(-4.2)slope

(- 5.1) (- 4.2)

Frequently Asked Questions (FAQ)

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