I would like to solve this indefinite integral. I was practicing figuring out integrals when this one stumped me. WolframAlpha seems to have calculated it using some numerical method. I feel like this should be solvable.
$$\int \frac{2^{x^2}}{5^x}dx$$
Thank you for any help.
Write it as $\int \exp[-(ax-bx^2)]dx$, complete the square in the exponent and change variable to $t=\sqrt{b}(x-a/2b)$. Then recognize that the integral is an error function.