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Popular Calculus >

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

Graph

Popular Examples

area x^3+x^2-6x,6x

a re a x^{3} + x^{2} - 6 x, 6 x

area f(x)=x^2-4,[-4,3]

a re a f (x) = x^{2} - 4, [- 4, 3]

integral of x-5

\int x - 5 d x

derivative of x^3(x-1^2)

\frac{d}{d x} (x^{3} (x - 1)^{2})

tangent of y=(3sqrt(x)+x)(2-x^2)

t an g e n t y = (3 x + x) (2 - x^{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