What is the integral of e^{(x-1)^2} ?

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

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integral of e^{(x-1)^2}

\int e^{(x - 1)^{2}} d x

\frac{π}{2} erfi (x - 1) + C

Solution steps

\int e^{(x - 1)^{2}} d x

Apply u-substitution

: \int e^{u^{2}} d u

= \int e^{u^{2}} d u

Use the nonelementary integral:

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

= \frac{π}{2} erfi (u)

Substitute back

u = x - 1

= \frac{π}{2} erfi (x - 1)

Add a constant to the solution

= \frac{π}{2} erfi (x - 1) + C

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