Integrating 3x^2*ln(x) - Is This Process Correct?

[feynmanpoint]

I was working on a question and would this work?

∫3x^2*ln(x)

After I did all of the math, I got to:

∫3x^2*ln(x)=x^3*ln(x)-x^3/3+c

The problem I am having is not with the actual integration but another step I took:

∫3x^2*ln(x)=x^3*(ln(x)-1/3+c)

I figured that -1/3+c just makes another constant so I left it as:

x^3*(ln(x)+c)

and distributing x^3 renders:

x^3*ln(x)-c*x^3

Is this process correct?

 

[TheoMcCloskey]

No problem combining constants, HOWEVER - Why did you take that other step (from 2nd equation to third)? That is, why do you think that other step is correct?

 

[feynmanpoint]

No problem combining constants, HOWEVER - Why did you take that other step (from 2nd equation to third)? That is, why do you think that other step is correct?

I now realize I was wrong. I factored out an x^3 even though it didn't have one making my conclusion worthless.