What is the integral of 5^{3x^2} ?

The integral of 5^{3x^2} is (sqrt(pi))/(2sqrt(3)\sqrt{ln(5))}\erfi(sqrt(ln(125))x)+C

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integral of 5^{3x^2}

\int 5^{3 x^{2}} d x

\frac{π}{2 3 ln ( 5 )} erfi (ln (125) x) + C

Solution steps

\int 5^{3 x^{2}} d x

Simplify

5^{3 x^{2}} : 12 5^{x^{2}}

= \int 12 5^{x^{2}} d x

Use the nonelementary integral:

\int 12 5^{x^{2}} d x = \frac{π erfi ( x ln ( 125 ) )}{2 ln ( 125 )}

= \frac{π erfi ( x ln ( 125 ) )}{2 ln ( 125 )}

Simplify

\frac{π erfi ( x ln ( 125 ) )}{2 ln ( 125 )} : \frac{π}{2 3 ln ( 5 )} erfi (ln (125) x)

= \frac{π}{2 3 ln ( 5 )} erfi (ln (125) x)

Add a constant to the solution

= \frac{π}{2 3 ln ( 5 )} erfi (ln (125) x) + C

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What is the integral of 5^{3x^2} ?
The integral of 5^{3x^2} is (sqrt(pi))/(2sqrt(3)\sqrt{ln(5))}\erfi(sqrt(ln(125))x)+C