$$\int \frac{1}{x\sin x}dx$$
Is this integral computable? I tried with Wolfram Alpha; it says
2026-04-29 18:13:54.1777486434
How do I evaluate the integral $\int \frac{1}{x\sin x}dx$?
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As another answer pointed out, this can't be computed in terms of elementary functions. In general, you can use the Risch algorithm to determine if a function has an anti-derivative expressible in terms of elementary functions (see e.g. http://en.wikipedia.org/wiki/Risch_algorithm ) and the Risch algorithm correctly identifies this example as not being integrable in terms of elementary functions.