don't know hot to integrate and do this question. I integrated it by parts then got to integrate (x^2/ 2 + 2x^2) again..
Not sure what you mean, but parts is right (for question a). Integrate x, differentiate arctan x, then integrate 1/2 x^2 all over 1 + x^2, which is equal to
which you can split into
Just in case a picture helps...
More in a tic
... is the product rule. Straight lines differentiate downwards (integrate up) with respect to x.
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!