kill(all)$fpprintprec:4$

van=facebook.com/LearningCalculus$

"(1/2)!" = %Gamma(3/2) ;
"(1/2)!" = '(integrate(sqrt(log("1/x")),x,0,1));

f(x):=sqrt(log(1/x))$

'integrate(f(x),x,0,1)=''(fullratsimp(integrate(f(x),x)))+C;

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

limit(F(1)-F(a),a,0,plus);

C:1;

g(x):=''(float(horner(logcontract(fullratsimp(taylor(F(x),x,1/2,6))))));

plot2d([f(x),g(x)], [x,0.01,1.99], [y,0.01,1.99])$