Symbolic Integration Problem of Univariate Expression : Integral 1/x to ln(x) + c

I just wrote a very simple integral like this:

clear, clc

syms x
f = 1/(3*x +1)
int(f)

And I got the wrong result as image below.

Did I do something wrong? Is there anything i should know about this?

Thanks.

Answer 1

[Diwakar Ravichandran]

Hi Herwin,

So going through your question,

Both the answers are correct. So, to clarify what I mean,

In your question you have mentioned that integral(1/x)=ln(x)+ C;

It is this C that plays a major role in both the answers.

If you take the answer that MATLAB has given you and take LCM(Least Common Multiple) of the term inside the log function, you get

 ans=(log((3x+1)/3))/3 right?

By properties of logarithms, we have log(a/b)=log(a)-log(b);

So the answer can be written as

 ans= (log(3x+1)-log 3)/3;

When you split the terms inside the parenthesis you get

 ans= (log(3x+1)/3)-(log 3)/3;

log(3)/3 is a constant and shows in your answer as a part of C (The constant of Integration).

Hope this helps,

Cheers!

[Herwin k]

Hi, Ravi

So the way I see it, Matlab assuming the Constant integration value based on LCM inside log function, since we don't know the C value is.

Well, thanks for the explanation.