What is the integral of (1-x)e^{x^2} ?

The integral of (1-x)e^{x^2} is (sqrt(pi))/2 \erfi(x)-1/2 e^{x^2}+C

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

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

\frac{π}{2} erfi (x) - \frac{1}{2} e^{x^{2}} + C

Solution steps

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

Expand

(1 - x) e^{x^{2}} : e^{x^{2}} - e^{x^{2}} x

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

\int e^{x^{2}} d x = \frac{π}{2} erfi (x)

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

= \frac{π}{2} erfi (x) - \frac{1}{2} e^{x^{2}}

Add a constant to the solution

= \frac{π}{2} erfi (x) - \frac{1}{2} e^{x^{2}} + C

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