Question

Solve the following integral:

ln (x+3)
----------
x + 3

Answer 1

Would I let (x+3) = u?

Answer 2

that may work...
better is to substitute : ln(x+3) = u

Answer 3

Yes but then I am unsure of what to do with the bottom.

Answer 4

ln(x+3) = u

differentiate both sides

1
----- dx = du
x+3

Answer 5

right ?

Answer 6

Yep got to that step

Answer 7

So then I would have
u 1
---- --------
X+3 X + 3

Answer 8

\(\large \mathbb{\int \frac{\ln(x+3)}{x+3}dx}\)

substitute \(\large \mathbb{\ln(x+3) = u}\)

differentiate both sides

\(\large \mathbb{\frac{1}{x+3} dx = du}\)

so the integral becomes :

\(\large \mathbb{\int u~ du }\)

Answer 9

next evaluate the integral...

Answer 10

U^2/2

Answer 11

ANd sub back in

Answer 12

yes !

Answer 13

Ahhh the x+3 's cancel

Thanks!!

Answer 14

np.. u wlc :)