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Popular >

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

Popular Examples

integral of r^2sin(θ)

\int r^{2} sin (θ) d r

integral of sin^2(1/2)x

\int sin^{2} (\frac{1}{2}) x d x

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

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

integral of 1/(-v^2+1)

\int \frac{1}{- v ^{2} + 1} d v

derivative of 8csc(5x^4-8x+6)derivative of

8 csc (5 x^{4} - 8 x + 6)

Frequently Asked Questions (FAQ)

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