kill(all)$

van=facebook.com/LearningCalculus$

u(x):= x*sin(x)+cos(x)$
v(x):=-x*cos(x)+sin(x)$

f(x,a,b):=x^2/(a*u(x)+b*v(x))^2;

f(x,a,b);

trigrat(integrate(f(x,a,b),x));

F(x,a,b):=''(trigrat(integrate(f(x,a,b),x)))$

F(x,r*cos(t),r*sin(t));

f(x,r*cos(t),r*sin(t));