Both solutions seem to be correct

[OutBoxer024]

I'm confused as both solutions seem to be correct but they give two different answers

 

[lookagain]

View attachment 37791
I'm confused as both solutions seem to be correct but they give two different answers

In the third line down on the left-hand side, you are missing a (1/3) multiplier in front of the integral.

The answer at the bottom right of the paper can be rewritten as

$\displaystyle \dfrac{ ln|3(x + 3)|}{3} \ + \ C_1 \ =$

$\displaystyle \dfrac{ln|3| \ + \ ln|x + 3|}{3} \ + C_1 \ =$

$\displaystyle \dfrac{ln|3|}{3} \ + \ \dfrac{ln|x + 3|}{3} \ + \ C_1 \ =$

$\displaystyle \dfrac{ln|x + 3|}{3} \ + \ \ \bigg(C_1 \ + \ \dfrac{ln|3|}{3}\bigg) \ =$

$\displaystyle \dfrac{ln|x + 3|}{3} \ + \ C$


This is true because $\displaystyle \ \dfrac{ln|3|}{3} \$ is a constant, and $\displaystyle \bigg( \ C_1 \ + \ \dfrac{ln|3|}{3} \bigg) \$ is a new constant,
which can be renamed as "C."

 

[Steven G]

Whenever this happens just check to see if your results differ by a constant.