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$\int_{\frac{1}{2014}}^{2014}\frac{\arctan x}{x}\text{d}x$

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    integrating from $\frac1{2014}$ to $2014$? – 2017-01-15
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    And what did you try? Why can't you do it? Where do you get stuck? – 2017-01-15

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Here's a hint: $\arctan(x) + \arctan(1/x) = \pi/2$ for $x > 0$. Try adding the integral to itself (perhaps with some changes to it by substitution).

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    No, we can't assume arctan(x) is constant - only that arctan(x) + arctan(1/x) is. But, notice that $\int_{1/2014}^{2014} \arctan(x) dx + \int_{1/2014}^{2014} \arctan(1/x) dx = \int_{1/2014}^{2014} \arctan(x) + \arctan(1/x) dx$ – 2017-01-15
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    Are you trying to re-format the question? – 2017-01-15