What is the integral of 3x^2e^{x^2} ?

The integral of 3x^2e^{x^2} is 3(1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x))+C

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integral of 3x^2e^{x^2}

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x^{2} e^{x^{2}} d x

Simplify

x^{2} : xx

= 3 \cdot \int xx e^{x^{2}} d x

Apply Integration By Parts

= 3 (\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)

= 3 (\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x))

Add a constant to the solution

= 3 (\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)) + C

What is the integral of 3x^2e^{x^2} ?
The integral of 3x^2e^{x^2} is 3(1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x))+C