Question

Use integration by parts to find the integrals in Exercise. ∫(6x+3)e-2x dx.

Answer 1

Answer:

-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)