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

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

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integral of 2e^{y^2}

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

π erfi (y) + C

Solution steps

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

Take the constant out:

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

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

Use the nonelementary integral:

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

= 2 \cdot \frac{π}{2} erfi (y)

Simplify

2 \cdot \frac{π}{2} erfi (y) : π erfi (y)

= π erfi (y)

Add a constant to the solution

= π erfi (y) + C

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