What is the integral of xe^{x^2}-x ?

The integral of xe^{x^2}-x is 1/2 e^{x^2}-(x^2)/2+C

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integral of xe^{x^2}-x

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

\frac{1}{2} e^{x^{2}} - \frac{x ^{2}}{2} + C

Solution steps

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

\int x e^{x^{2}} d x = \frac{1}{2} e^{x^{2}}

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

= \frac{1}{2} e^{x^{2}} - \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} - \frac{x ^{2}}{2} + C

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What is the integral of xe^{x^2}-x ?
The integral of xe^{x^2}-x is 1/2 e^{x^2}-(x^2)/2+C