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

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

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integral of e^{x^2}y

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

y \frac{π}{2} erfi (x) + C

Solution steps

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= y \frac{π}{2} erfi (x)

Add a constant to the solution

= y \frac{π}{2} erfi (x) + C

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