log rule for integration confusion

If I have a function:

f(x) = 1 / (x+1), and I want to find it's indefinite integral, I can apply the log rule and get:

F(x) = ln |x+1| + C

If, however, I multiply both the numerator and the denominator by 2, before integrating, I get:

f(x) = 1 / (x+1) = 2 / 2x + 2

F(x) = ln |2x+2| + C

Clearly, f(x) are equal in both cases, but I can't see how ln |2x+2| equals ln |x+1|

Any explanation? Thanks

Re: log rule for integration confusion

Re: log rule for integration confusion

If you write:

Because is also an constant number you can say:

with a new constant integration term.

Re: log rule for integration confusion

Quote:

Originally Posted by

**gralla55** f(x) = 1 / (x+1), and I want to find it's indefinite integral, I can apply the log rule and get: F(x) = ln |x+1| + C

F(x) = ln |2x+2| + C

Clearly, f(x) are equal in both cases, but I can't see how ln |2x+2| equals ln |x+1|

Your mistake in using the same constant, i.e. they are different constants.

Recall that .

If is the constant in the first then is in the second.

Re: log rule for integration confusion