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

Popular >

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

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

\int \frac{1}{( 9 - x ^{2} ) ^{3}} d x

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

\int x^{3} e^{- 4 x^{2}} d x

\int \frac{5 x ^{2} - 5}{x ^{2}} d x

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