1 method:

(%i1) integrate(2^(-x),x,0,1);

(%o1) integrate(1/2^x,x,0,1)

(%i2) changevar(%, log(y)/log(2)=x, y, x);

(%o2) integrate(1/y^2,y,1,2)/log(2)

(%i3) ev(%, nouns);

(%o3) 1/(2*log(2))

2 method:

(%i4) risch(1/2^x, x);

(%o4) -%e^(-log(2)*x)/log(2)

(%i5) ev(%,x=1)-ev(%,x=0);

(%o5) 1/(2*log(2))

(%i6) float(%);

(%o6) 0.72134752044448

3 method:

(%i7) quad_qags(1/2^x, x, 0, 1);

(%o7) [0.72134752044448,8.008566259537295*10^-15,21,0]