I was trying to solve the integration of $\int \sin(x) e^{\sin(x)-x} (\sin(x)-x) dx$ with integration by parts, but with no success.

I also tried to expend the expression to:

$\int \sin^2(x) e^{\sin(x)-x} dx - \int x\sin(x) e^{\sin(x)-x} dx$

Also this didn't really help. Maybe someone has better ideas?

  • $\begingroup$ where did you found this integral? $\endgroup$ – Dr. Sonnhard Graubner Apr 10 '15 at 11:56
  • $\begingroup$ It doesn't have any antiderivative. Even W|A can't integrate it. $\endgroup$ – Prasun Biswas Apr 10 '15 at 11:59
  • $\begingroup$ @PrasunBiswas I have seen many times in the past where a solution exists that wolfram cannot find... $\endgroup$ – jm324354 Apr 10 '15 at 12:10
  • $\begingroup$ @ Dr. Sonnhard Graubner, the integral is the outcome of a mathematical model, which intends to describe the average number of neighbors of a single node/host in a given network. $\endgroup$ – ChunleiA Apr 10 '15 at 12:26
  • $\begingroup$ @jm324354, totally agree. if W|A could solve this directly, then I don't have to post it here ;) Also tools like wxMaxima could not solve it directly. But I think with some steps of simplifications it should be solvable by the machines ... $\endgroup$ – ChunleiA Apr 10 '15 at 12:31

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