kill(all)$ fpprintprec:4$

     Van | facebook.com/LearningCalculus | 2015

a(x):=cos(x)^2*sin(4*x)$
b(x):=sin(x)^2*sin(4*x)$

'integrate(a(x),x) = ratsimp(integrate(a(x),x));
'integrate(b(x),x) = ratsimp(integrate(b(x),x));

A(x):=(2*sin(x)^6-3*sin(x)^4-2*cos(x)^6)/3$
B(x):=-(4*sin(x)^6-3*sin(x)^4)/3$

A:A(%pi/2)-A(%pi/4)$
B:B(%pi/2)-B(%pi/4)$
[A, B, A-B, A+B, B/A, B*A];