w1, s1, w2, s2, ae, x = var('w1, s1, w2, s2, ae, x ')
N1=1-3*x*x+2*x*x*x
N2=(x*(1-2*x+x*x))*ae
N3=3*x*x-2*x*x*x
N4=(x*x*x-x*x)*ae
N1d1=6*x*x-6*x
N2d1=(3*x*x-4*x+1)*ae
N3d1=6*x-6*x*x
N4d1=(3*x*x-2*x)*ae
N1d2=12*x-6
N2d2=(6*x-4)*ae
N3d2=6-12*x
N4d2=(6*x-2)*ae
f1=N1d1
f2=N2d1
f3=N3d1
f4=N4d1
kk11=f1*f1
kk12=f1*f2
kk13=f1*f3
kk14=f1*f4
kk21=f2*f1
kk22=f2*f2
kk23=f2*f3
kk24=f2*f4
kk31=f3*f1
kk32=f3*f2
kk33=f3*f3
kk34=f3*f4
kk41=f4*f1
kk42=f4*f2
kk43=f4*f3
kk44=f4*f4
k11=integral(kk11, x, 0, 1)
k12=integral(kk12, x, 0, 1)
k13=integral(kk13, x, 0, 1)
k14=integral(kk14, x, 0, 1)
k21=integral(kk21, x, 0, 1)
k22=integral(kk22, x, 0, 1)
k23=integral(kk23, x, 0, 1)
k24=integral(kk24, x, 0, 1)
k31=integral(kk31, x, 0, 1)
k32=integral(kk32, x, 0, 1)
k33=integral(kk33, x, 0, 1)
k34=integral(kk34, x, 0, 1)
k41=integral(kk41, x, 0, 1)
k42=integral(kk42, x, 0, 1)
k43=integral(kk43, x, 0, 1)
k44=integral(kk44, x, 0, 1)
print k11;print k12;print k13;print k14;
print k21;print k22;print k23;print k24;
print k31;print k32;print k33;print k34;
print k41;print k42;print k43;print k44;
show(k11);show(k12);show(k13);show(k14);
show(k21);show(k22);show(k23);show(k24);
show(k31);show(k32);show(k33);show(k34);
show(k41);show(k42);show(k43);show(k44);