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

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

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

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

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

Solution steps

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

Simplify

x^{2} : xx

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

Apply Integration By Parts

= \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

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