What is the integral from 0 to 2x of e^{t^2} ?

The integral from 0 to 2x of e^{t^2} is (sqrt(pi))/2 \erfi(2x)

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integral from 0 to 2x of e^{t^2}

\int_{0}^{2 x} e^{t^{2}} d t

\frac{π}{2} erfi (2 x)

Solution steps

\int_{0}^{2 x} 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)]_{0}^{2 x}

Compute the boundaries:

\frac{π}{2} erfi (2 x)

= \frac{π}{2} erfi (2 x)

\int_{\frac{π}{6}}^{\frac{π}{4}} sin (x) d x

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\int_{0}^{3} \frac{x e ^{x}}{( 1 + x ) ^{2}} d x

\int_{y}^{\infty} e^{- x} d x

What is the integral from 0 to 2x of e^{t^2} ?
The integral from 0 to 2x of e^{t^2} is (sqrt(pi))/2 \erfi(2x)