I want to write a code in Fortran to solve this integral numerically: $$\int_{1095}^\infty \frac{dx}{x\sqrt{(x+644.153)(4.17 \cdot 10^{-5} x+0.145)}}$$ What is the best method for it?
I tried Monte-Carlo and RK4 but I had to put a big number instead of infinity.
To avoid infinity, I changed the variable $x$ to $1/t$. Then the integral becomes: $$\int_0^{1/1095}\frac{dt}{(t\sqrt{(1/t+644.153)(4.17 \cdot 10^{-5}/t+0.145)}}$$
But this time the problem is that the lower limit of the integral is one of the roots of the denominator. Can you suggest another way of changing variables to avoid this problem, too?