Найти интеграл ln^2 (x)dx

[latex]\int{ln^2x}\, dx = * \\ u=ln^2x \ ->du=\frac{2lnxdx}{x} \\ dv=dx \ ->v=x \\ *=xln^2x-\int{\frac{2xlnx}{x}}\, dx = xln^2x-2\int{lnx}\, dx=* \\ u=lnx \ ->du=\frac{dx}{x} \\ dv=dx \ ->v=x \\ =*xln^2x-2(xlnx-\int{\frac{x}{x}}\, dx) = xln^2x-2xlnx+2x +C[/latex]   Ответ:[latex] xln^2x-2xlnx+2x +C[/latex]