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Popular Calculus >

integral of xe-x

Solution

\int x e - x d x

Solution

\frac{e x ^{2}}{2} - \frac{x ^{2}}{2} + 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 e d x - \int x d x

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

slope of (-4,2),(-9,-10)

s l o p e (- 4, 2), (- 9, - 10)

sum from n=0 to infinity of-1/(3^n)

n = 0 \sum \infty - \frac{1}{3 ^{n}}

derivative of sec^2(x-4)

\frac{d}{d x} (sec^{2} (x) - 4)

derivative of arcsin(x/5)

d er i v a t i v e arcsin (\frac{x}{5})

integral of (x^2)/(x^3+5)

\int \frac{x ^{2}}{x ^{3} + 5} d x

Frequently Asked Questions (FAQ)

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