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

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

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integral of e^{x^2}-1

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

\frac{π}{2} erfi (x) - x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{x^{2}} d x - \int 1 d x

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

\int 1 d x = x

= \frac{π}{2} erfi (x) - x

Add a constant to the solution

= \frac{π}{2} erfi (x) - x + C

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