how to integrate arc tangent x

Question

i don't know what are the techniques in integrating in calculus

Answer 1

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

Answer 2

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