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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 a^2-x^2

\int a^{2} - x^{2} d x

integral of (x^2)/((4x^2-4x-3)^{3/2)}

\int \frac{x ^{2}}{( 4 x ^{2} - 4 x - 3 ) ^{\frac{3}{2}}} d x

integral of (sqrt(5-3tan(x)))/(cos^2(x))

\int \frac{5 - 3 tan ( x )}{cos ^{2} ( x )} d x

integral of (-4x)/((2-2x^2)^3)

\int \frac{- 4 x}{( 2 - 2 x ^{2} ) ^{3}} d x

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

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