[sDIY] ot integrating ln(x)

[Martin Czech]

You were asking two questions:

Int{ln(x)}dx = x*ln(x)-x+C
      f(x)        F(x)

You can show this by simple differentiation of F(x)

d/dx F(x)=f(x)

Next:

ln(f(x)) means "chaining" of functions, I do not know the proper term.
Unfortunetaly there exists no rule for integration of chained functions
(it exists for differentiation).
So, for every f(x) you will have to take a look into a good table
of integrals and hope that you will find it. If not, well that's it.
You'll most probably not be able to find an analytical solution.

There are little books like "the Bronstein" (Bronstein/Semendjajew)
which contain nearly all the math you will ever need on say , 700 pages.
Get such a good book, it's a bargain.

m.c.