What is the integral of e^{x^2}x^2 ?

The integral of e^{x^2}x^2 is 1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x)+C

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integral of e^{x^2}x^2

integral

e^{x^{2}} x^{2}

\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + C

Solution steps

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

Simplify

x^{2} : xx

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

Apply Integration By Parts

: \frac{1}{2} e^{x^{2}} x - \int \frac{1}{2} e^{x^{2}} d x

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

\int \frac{1}{2} e^{x^{2}} d x = \frac{π}{4} erfi (x)

= \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + C

3 x^{2} - 9 x + 5

\frac{e ^{x}}{3}

\frac{1}{5 x}

e^{x} + \frac{1}{2} + 2 x^{2} + 3

\frac{1}{x ^{2} + 9}

What is the integral of e^{x^2}x^2 ?
The integral of e^{x^2}x^2 is 1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x)+C