What is the integral from-2 to x^2-3x of e^{x^2} ?

The integral from-2 to x^2-3x of e^{x^2} is (sqrt(pi))/2 \erfi(x^2-3x)-(sqrt(pi))/2 \erfi(-2)

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integral from-2 to x^2-3x of e^{x^2}

\int_{- 2}^{x^{2} - 3 x} e^{x^{2}} d x

\frac{π}{2} erfi (x^{2} - 3 x) - \frac{π}{2} erfi (- 2)

Solution steps

\int_{- 2}^{x^{2} - 3 x} e^{x^{2}} d x

Use the nonelementary integral:

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

= [\frac{π}{2} erfi (x)]_{- 2}^{x^{2} - 3 x}

Compute the boundaries:

\frac{π}{2} erfi (x^{2} - 3 x) - \frac{π}{2} erfi (- 2)

= \frac{π}{2} erfi (x^{2} - 3 x) - \frac{π}{2} erfi (- 2)

\int_{- 1}^{4} (x + 1) d x

\int_{0}^{2 π} sin^{2} (2 t) d t

\int_{0}^{2} 3 x^{2} - 2 d x

\int_{- 2}^{2} x^{4} + 5 x^{2} + 2 x + 8 d x

\int_{0}^{1} y^{2} 30 y^{2} (1 - y)^{2} d y

What is the integral from-2 to x^2-3x of e^{x^2} ?
The integral from-2 to x^2-3x of e^{x^2} is (sqrt(pi))/2 \erfi(x^2-3x)-(sqrt(pi))/2 \erfi(-2)