Integral gives wrong answer

Hello Frank, This might be more of an observation than an answer, but one point not in your favor is that since log10(x) = log(x)/log(10), your entire integral is proportional to 1/log(10):

Int = (1/log(10)) * [ -x * (1/2) * int(log(x)/x^2) + (1/2)*x^3 * int(log(x)/x^4) ]

With the annoying log10 behavior out of there, the rest of the integral is

(1/3)log(x) + 4/9

and the entire answer is what your symbolic math programs are saying. However, there are a couple of indefinite integrals here and it's possible that there is an additional constant floating around having to do with the lower limit for x in the integrals (and of course things also depend on whether you are using log or log10 in the ODE).

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Walter Roberson 2017-1-5

I did some searching a couple of months ago, and I had difficulty finding a programming language which used ln() or loge() for natural log; all the ones I checked used log() for natural log.

Frank Hansper 2017-1-7

编辑：Frank Hansper 2017-1-7

I will remember that. Matlab is my "first" encounter with programming language (pl), so my experience with others is limited. The reason I was confused is that my advisor is fond of solving integrals by hand, so I was puzzled to see log as ln (expecting him not to write in pl).

I have talked to him now and he said: "In my world log = ln", so it was a misunderstanding and my question is now all cleared out.

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