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I want to prove the inequality $3x\cdot \mathrm{arccot}{x}\geq\ln(1+x^{2})$... using Cauchy's theorem..I saw this in a book which I bought in a library and ive never seen this type of exercise..can you solve it ?

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You can find some good starting points on how to format mathematics on the site here and here. This AMS reference is very useful. If you need to format more advanced things, there are many excellent references on LaTeX on the internet, including StackExchange's own TeX.SE site. – Zev Chonoles Dec 26 '12 at 21:25

You may need to modify the function, or the interval. Compute $3x\,\text{arccot}\,x-\ln(1+x^2)$ at $x=10$. The result is negative.

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It's true for $0 \le x \le 4.246876095$ approximately, not true outside that interval. What interval did you want to prove it on?

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