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feynmanpoint

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∫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?