kill(all)$

van=facebook.com/LearningCalculus$

f(x):=x^2/sqrt(1+x^6);

'integrate(f(x),x)=logcontract(fullratsimp(''(integrate(f(x),x))))+C ;

    Given that:

Asinh(u):=log(u+sqrt(u^2+1));

    and that 

Asinh(x^3)/3;

     Prove

ASinh(x^3/3) + C = C-log((sqrt(x^6+1)-x^3)/(sqrt(x^6+1)+x^3))/6;