Explicație pas cu pas:
[tex]\int\limits {x*ln^2x} \, dx =\int\limits {(x^2/2)'*ln^2x} \, dx=(x^2*ln^2 x)/2-\int\limits {x^2/2*2*lnx*1/x} \, dx=(x^2*ln^2 x)/2-\int\limits {x*lnx} \, dx =(x^2*ln^2 x)/2-\int\limits {(x^2)/2*lnx} \, dx=(x^2*ln^2 x)/2-(x^2*lnx)/2+\int\limits {x^2/2*1/x} \, dx=(x^2*ln^2 x)/2-(x^2*lnx)/2+\int\limits {x/2} \, dx=(x^2*ln^2 x)/2-(x^2*lnx)/2+x^2/4+C=(2x^2ln^2x-2x^2lnx+x^2)/4+C[/tex]
