∫  etan−1x(1+x+x2)  .  d(cot−1x)  is equal to

I=∫etan−1x  (1+x+x2)  -11+x2 dx     =−∫   etan−1x(1+x1+x2)dx     =−∫   etan−1xdx−∫  x . etan−1x1+x2 dx     =−∫   etan−1xdx−   x  .  etan−1x+  ∫  etan−1xdx+C      =−x . etan−1x+C