In order to use partial integration, the integral formula needs to be modified: ∫d(e3x)= e3x? d(3x)=3e^(3x)dx；

Compared with E (3x) DX, the former is 3 times more; Therefore, (1/3) d (E3x) = E3xdx;

∴∫xe^(3x)dx=( 1/3)∫xd(e^3x)=( 1/3)[xe^(3x)-∫e^(3x)dx]

=( 1/3)[xe^(3)-( 1/3)∫e^(3x)d(3x)]=( 1/3)[xe^(3x)-( 1/3)e^(3x)+c=( 1/3)[x-( 1/3)]e^(3x)+c；

Note: When dx is changed to d(3x), the integer symbol will be divided by 3, which is multiplied by1/3; Because d (3x) = 3dx;