What is the integral of (e^{x^2})/2 ?

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

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integral of (e^{x^2})/2

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

\frac{π}{4} erfi (x) + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{x^{2}} d x

Use the nonelementary integral:

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

= \frac{1}{2} \cdot \frac{π}{2} erfi (x)

Simplify

\frac{1}{2} \cdot \frac{π}{2} erfi (x) : \frac{π}{4} erfi (x)

= \frac{π}{4} erfi (x)

Add a constant to the solution

= \frac{π}{4} erfi (x) + C

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