How do you use substitution to integrate 4 / ((3x + 6)^2) dx?

1 Answer
Apr 16, 2018

use the u substitution

u=3x+6

du=3dx

to get 4 multiply it by 4/3

4/3*du=4/cancel(3)*cancel(3)dx

4/3du=4dx

bring the integral into the u world

int(4/3)/u^2

bring the constant into the front

4/3int1/u^2

use the index law

1/y^z=y^-z

4/3intu^-2

use the power rule for integration and integrate

intx^n=x^(n+1)/(n+1)

=4/3intu^-2

4/3(u^(-2+1)/(-2+1))+C

4/3(u^(-1)/(-1))+C

bring it into the x world

4/3(-(3x+6)^-1)+C

4/3(-1/(3x+6))+C

finally multiply it

-4/(9x+18)+C