What is the integral from 0 to x^3 of e^{t^2} ?

The integral from 0 to x^3 of e^{t^2} is (sqrt(pi))/2 \erfi(x^3)

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integral from 0 to x^3 of e^{t^2}

\int_{0}^{x^{3}} e^{t^{2}} d t

\frac{π}{2} erfi (x^{3})

Solution steps

\int_{0}^{x^{3}} 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}^{x^{3}}

Compute the boundaries:

\frac{π}{2} erfi (x^{3})

= \frac{π}{2} erfi (x^{3})

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\int_{0}^{1} π (x^{4} - x^{2}) d x

\int_{0}^{\frac{π}{2}} e^{x} sin^{2} (x) d x

\int_{0}^{2} 3 x 4 - x^{2} d x

What is the integral from 0 to x^3 of e^{t^2} ?
The integral from 0 to x^3 of e^{t^2} is (sqrt(pi))/2 \erfi(x^3)