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

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

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integral of y^2e^{y^2}

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

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

Solution steps

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

Simplify

y^{2} : yy

= \int yy e^{y^{2}} d y

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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