Hey people, I just came up across something I didn't know about in my revision. Say I want to find the integral
Normally I would do this as following
However, is it not true that I can also make this of the form
which via a simple u sub yields
Which does not seem to be equivalent to the original answer. Is it the case that both are valid, but the constants k and j are different? Is k=j+ln3?
Also, how would I go about expressing the answers
as explicit functions of x?