How do you solve the integral of ln(x)

This will use the process of integration by parts.

First, notice that ln(x)=ln(x)*1.

So, the integral of ln(x) is the integral of ln(x)*1. The process of integration by parts is;  int(v*du/dx)dx=vu - int(dv/dx*u)dx.

Set ln(x)=v, 1=du/dx, so int(ln(x)*1)dx = ln(x)*x - int(1/x*x)dx = x*ln(x)-int(1)dx = x*ln(x)-x+constant.

And you're done!

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