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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 (x+2)^6

\int (x + 2)^{6} d x

integral of (cot(x)csc(x))/(csc^7(x))

\int \frac{cot ( x ) csc ( x )}{csc ^{7} ( x )} d x

integral of e^{-x}cos(npix)

\int e^{- x} cos (nπ x) d x

integral of 1/(ln^3(x))

\int \frac{1}{ln ^{3} ( x )} d x

integral of x(x^2+4)^{1/2}

\int x (x^{2} + 4)^{\frac{1}{2}} 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