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

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

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integral of xe^x-xe^{x^2}

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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