kill(all)$

van=facebook.com/LearningCalculus$

u(x):=x*sin(x)$

f: lambda([x], u(x))$

F(f,x,A,B):=''(integrate(f(x),x,A,B))$

'integrate(f(x),x,0,a)=F(f,x,0,a);

'integrate(f(a-x),x,0,a)=F(f,a-x,0,a);

assume(a > 0)$

van=facebook.com/LearningCalculus$

'(integrate(f(x),x,0,a)) = '(integrate(f(a-x),x,0,a));

f(x):=factor(x^3*cos(x)^4*sin(x))$

g(x):=factor(%pi^2-3*%pi*x+3*x^2)$

h(x):=''(f(x)/g(x));

f(x)/g(x)+f(%pi-x)/g(%pi-x);

h(x):=fullratsimp(f(x)/g(x)+f(%pi-x)/g(%pi-x))/2$ h(x);

integrate(h(x),x);

integrate(h(x),x,0,%pi);

float(%);