Two solutions for same problem dont match ?

[Miike012]

I was integrating and I noticed that if I integrate one way I get a diff answer than if I integrated another way... My work is in the paint document. I followed all the correct algebraic prodedures I believe... but anyways which one is incorrect?

 

[tiny-tim]

Hii Miike012!

Your two solutions are

x - 6 + 6ln(x - 6) + C

and x + 6ln(x - 6) + C​

They're the same!

(different C )

 

[awkward]

Your answers are the same.

If C is an arbitrary constant, then C-6 is also an arbitrary constant.

(Beaten to the punch by tiny-tim.)