Integral of $\exp(-\frac{c_1}{x}-\frac{c_2}{x^2})$ on positive real line Is it possible to find
$$
\int_{0}^{K}
\exp\left(-\,{c_{1} \over x} - {c_{2} \over x^{2}}\right)
\,\mathrm{d}x
$$
or at least a good approximation to it, where $c_{1}$ and $c_{2}$ are positive and $K$ is a very large number $?$.
I tried to consider the change of variables
$-u = -c_{1}/x - c_{2}/x^{2}$ but to no avail.
Note: Approximation can include known functions such as Erf, or Gamma, if necessary.

As said, series expansion could be the solution. Writing
$$\exp\left(-\frac{a}{x}-\frac{b}{x^2}\right)=1+\sum_{n=1}^p \frac {c_n}{n! \,x^n}=f(x)$$ the $c_n$'s would be
$$\left(
\begin{array}{cc}
 1 & -a \\
 2 & a^2-2 b \\
 3 & -a^3+6 a b \\
 4 & a^4-12 b a^2+12 b^2 \\
 5 & -a^5+20 b a^3-60 b^2 a \\
 6 & a^6-30 b a^4+180 b^2 a^2-120 b^3 \\
 7 & -a^7+42 b a^5-420 b^2 a^3+840 b^3 a \\
 8 & a^8-56 b a^6+840 b^2 a^4-3360 b^3 a^2+1680 b^4 \\
 9 & -a^9+72 b a^7-1512 b^2 a^5+10080 b^3 a^3-15120 b^4 a \\
 10 & a^{10}-90 b a^8+2520 b^2 a^6-25200 b^3 a^4+75600 b^4 a^2-30240 b^5
\end{array}
\right)$$ and
$$\int\exp\left(-\frac{a}{x}-\frac{b}{x^2}\right)\,dx=1-a\log(x)-\sum_{n=2}^p \frac {c_n}{(n-1)\,n! \,x^{n-1}}+ C$$
For sure, there is a  problem with a lower bound equal to $0$.
