Use integration by parts to find the integrals in Exercise.

∫ (6x+3) e-2x dx.

-3e^-2x (x+1)

Step-by-step explanation:

formula of byparts integration:

g (x) ∫f (x) dx-∫∫f (x). d/dx (g (x)) dx

= (6x+3) ∫e^-2x dx-∫∫e^-2x. d/dx (6x+3) dx

= (6x+3) ((e-2x) / -2) - ∫ (e^-2x) / -2.6 dx

= (6x+3) ((e-2x) / -2) + 3 (e^-2x) / -2

= (6xe-2x+3e-2x+3e-2x) / -2

= (6xe-2x+6e-2x) / -2

=6e^-2x (x+1) / -2

=-3e^-2x (x+1)