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

The integral of 4^{x^2} is (sqrt(pi))/(2sqrt(2)\sqrt{ln(2))}\erfi(sqrt(ln(4))x)+C

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integral of 4^{x^2}

\int 4^{x^{2}} d x

\frac{π}{2 2 ln ( 2 )} erfi (ln (4) x) + C

Solution steps

\int 4^{x^{2}} d x

Use the nonelementary integral:

\int 4^{x^{2}} d x = \frac{π erfi ( x ln ( 4 ) )}{2 ln ( 4 )}

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

Simplify

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

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

Add a constant to the solution

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

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