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

via

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?

Mr F says: They are equivalent. j + ln 3 is just as arbitrary as k .....
Also, how would I go about expressing the answers

and

as explicit functions of x?

Mr F says: They already are explicit functions of x. Do you mean how to express them as explicit functions of y ....?
Ta muchly.