The Hardest Integral I’ve Ever Done
The Hardest Integral I’ve Ever Done

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When we were with my friends, doing a math bee, I wrote this question randomly. However, we couldn’t solve it for 3 hours straight, even symbolab couldn’t. The logarithm’s base is inseparable (exists in complex plane), we have tried substitution however lead to insane complex stuff. At this point we have no idea what to do. Maybe we are way too bad? Also, we have thought that this may be a function which cannot be obtainable during integration of a function in ℝ, due to the logarithm’s base. Which one is it? If it is solvable, how?

Note: the first version was the 2nd equation, I have then changed it to the first one. Maybe second one might be more solvable due to having an actual number rather than all these variables.

Also, if these are not solvable what about these ones?

2nd Note: To state my question clearer, how can we modify the inside of the integral to make it solvable by known integration forms such as integral of cos(x), integral of ln(x), integral of 1/x. If we cannot change this to a form that is much more simpler, the question changes to, are there functions that are not obtainable by differentiation. I brought up this question during a summer school and our attempts are pictured, even though they were, they were not anything of significance.

Also, this was Wolfram Alpha’s response

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