Basic logarithmic expression

As a result of looking for the analytical solution to the following indefinite integral

I came to the following expression:

for being the integration constant. I am trying now to get the expression of and I am not sure about the following steps:

1) Multiply both terms by -1 (not sure if this is valid with logarithmic expressions):

2) Apply exponentiation to both sides of the previous expression:

Since is a constant ( ), I am not sure how to proceed further. , I would try something like:

But this is not correct. I would appreciate if somebody would give a hint.

Thank you in advance.

Re: Basic logarithmic expression

What, exactly, are you trying to say? Yes is the general solution to the integration. But what does "for C" mean?

Re: Basic logarithmic expression

I re-edited the post again...

Re: Basic logarithmic expression

Re: Basic logarithmic expression

Quote:

Originally Posted by

**HallsofIvy** What, exactly, are you trying to say? Yes

is the general solution to the integration. But what does "for C" mean?

Actually, it's .

Re: Basic logarithmic expression

Hi everybody!

You guys helped me a lot!. I figured out how to reach to the solution. I'll post it here just in case somebody need it!

From the original expression:

by separating the variables we have:

with substitution of , I get that

To obtain the following expression to be solved by direct integration:

whose solution is:

for being the integration constant. Thanks **Prove It** for your excellent post about it!

Now it's simple to follow **Soroban**:

, this was the difficult step for me :S

, now let

Thanks so much !!!

Re: Basic logarithmic expression

Quote:

Originally Posted by

**jguzman** Hi everybody!

You guys helped me a lot!. I figured out how to reach to the solution. I'll post it here just in case somebody need it!

From the original expression:

by separating the variables we have:

with substitution of

, I get that

To obtain the following expression to be solved by direct integration:

whose solution is:

for

being the integration constant. Thanks

**Prove It** for your

excellent post about it!

Now it's simple to follow

**Soroban**:

, this was the difficult step for me :S

, now let

Thanks so much !!!

The final answer is correct, just a couple of notes. You can't just disregard the absolute value.

Re: Basic logarithmic expression

Re: Basic logarithmic expression

It's fine to have just one sign for the K, since the fact that plus or minus a constant is still a constant. I just wanted to point out what happens to the absolute value in the solving for x.