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Popular >

integral of xe^x+x

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (xe^x)/((1+e^x)^2)

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

integral of (e^{2x}+1/(1-x))

\int (e^{2 x} + \frac{1}{1 - x}) d x

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

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

integral of 1/(sqrt(-4x^2-20x-21))

\int \frac{1}{- 4 x ^{2} - 20 x - 21} d x

integral of (1+tan(x))/(sin(2x))

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

Frequently Asked Questions (FAQ)

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