Question

Help in integral:

x-3 + 6/(3x+2) dx. The author's answer is x^2/2-3x + 2ln|3x+2|+C.
I understand that the integral of x-3 is x^2/2-3x.
But why is the integral of 6/(3x+2) equal to : 2ln|3x+2|, where does the ln comes from?
thanks for your help.

Answer 1

the ln come from the 1/(3x+2) you substitute 3x+2 for u
u= 3x+2
du = 3 dx this changes the integral to 1/u* du/3

Answer 2

6/3 = 2 multiplied by the integral of 1/u which is ln|u|
you substitute back to give 2 ln|3x+2|

Answer 3

oops! + C

Answer 4

Thanks alot

Answer 5

yup