What is the integral from 0 to 4 of 2^{x^2} ?

The integral from 0 to 4 of 2^{x^2} is (sqrt(pi)\erfi(4sqrt(ln(2))))/(2sqrt(ln(2)))

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integral from 0 to 4 of 2^{x^2}

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

\frac{π erfi ( 4 ln ( 2 ) )}{2 ln ( 2 )}

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π erfi ( x ln ( 2 ) )}{2 ln ( 2 )}]_{0}^{4}

Compute the boundaries:

\frac{π}{2 ln ( 2 )} erfi (4 ln (2))

= \frac{π}{2 ln ( 2 )} erfi (4 ln (2))

Simplify

= \frac{π erfi ( 4 ln ( 2 ) )}{2 ln ( 2 )}

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What is the integral from 0 to 4 of 2^{x^2} ?
The integral from 0 to 4 of 2^{x^2} is (sqrt(pi)\erfi(4sqrt(ln(2))))/(2sqrt(ln(2)))