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how to integrate arc tangent x

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2 Answers

The answer given is a very nice application of integration by parts (see http://en.wikipedia.org/wiki/Integration_by_parts).  Bravo for that!  But it uses the derivative of the arctangent (which is not derived in the solution presented) - but you can find it at: http://www.coastal.edu/mathcenter/HelpPages/Handouts/invhyp.PDF
 
But you could also simply look up the formula for the artan integral at http://en.wikipedia.org/wiki/List_of_integrals_of_inverse_trigonometric_functions
Use integration by parts,
∫arctan x dx
= x arctan x - ∫x darctan x
= x arctan x - ∫x/(1+x^2) dx
= x arctan x - (1/2)ln(1+x^2) + c