34.8 (a) Use integration by parts to evaluate
∫ xּarctan x dx.
Hint: let u(x) = arctan x, so that u′(x) = 1/(1+x2).
(b) If you used v(x) = x2/2 in part (a), do the computation again with v(x) = (x2+1)/2. This interesting example is taken from J. L. Borman.
This shows how to use integration by parts with an arctan integral.