integrate(exp-(ax^{2}+bx)/x wrt x where x range from 0 to 5*10^{-9}
First, you are missing a ")". Did you intend "integrate(exp-(ax2+bx)/x) wrt x"?
Second, it looks like that cannot be integrated in terms of "elementary functions". Do you want a numerical integration or integral in terms of the "error function"?
your notation is very unclear
do you mean to integrate $\dfrac{e^{-(ax^2 + b x)}}{x}$ ?
or do you mean $e^{-\dfrac{a x^2 + b x}{x}}$
if the first case the integral doesn't converge on $[0, 5\times 10^{-9}]$
if the second case why not write $e^{-(a x + b)}$ and the answer is
$\displaystyle \int_0^{5\times 10^{-9}}e^{-(ax + b)}~dx = \dfrac{\left(1-e^{-\frac{a}{200000000}}\right) e^{-b}}{a}$