1.

Solve ∫ (cot (log x)/x) dx, x ∈ I ⊂ (0, ∞) \ {enπ : n ∈ Z).

Answer»

t = log x ⇒ dt = dx/x 

∫ (cot (log x)/x) dx = ∫ cot t dt = log (sin t) + C 

= log (sin (log x)) + C



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