Solve this integral problem. ...................................

2log cotx can be written as logcot^2x....There is a property....that...alogb = logb^a...So...the given integral becomes...Integral of e^logcot^2x....We have another property that e^loga = a...So the given integral is...From trigonometric relations...We have...cot^2(x) = csc^2(x)-1and the indefinite integral of csc^2(ax) = -cot(ax)/atherefore:the integral[cot^2(x)] = integral[csc^2(x)] - integral[1]which yields your answer of cotx - xHope you have understood this....