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I am struggling to solve the following definite integral in C: $int_{a1}^1 (0.4-0.5*a)/a da$, where the lower limit is very small a1=1e-14, upper limit is 1.0.

I know I can solve this analytically, but in general I have to solve for similar functions which do not have analytical integration result. I chose this function here because I can get the results (12.394...) analytically for error estimation.

I used many methods in C, like the Romberg method, but could not get the correct result. Interestingly, in python, scipy.integrate.quad gives very good result (error~1e-8) very quickly. But I need the routine in C, also it has to be very fast (comparable to scipy.integrate.quad). Can anyone help me finding the solution numerically in C? Thanks in advance.

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