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

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

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

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

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

Solution steps

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

Use the nonelementary integral:

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

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

Compute the boundaries:

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

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

\int 7 x + 2 d x

\frac{5 s e ^{- s}}{2 s ^{2} + 32}

\int \frac{x + 1}{( x + 2 ) ^{3}} d x

9 y^{^{''}} - 12 y^{^{'}} + 4 y = e^{- 3 x}

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

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