∫u is not defined.

In integration, the dx or du component is important.

∫1/x is not defined. But, ∫(1/x)dx = logx + c or lnx + c(as denoted in some textbooks).

Similarly, ∫(x^n)dx = [(x^n+1)/(n+1)] + c.]]>

Thanks again.

]]>let u= ln(x)

du/dx = 1/x or du = dx/x

replace dx/x with du

and ln(x) with u

then you are left with ∫ u du == u²/2

thats where the 2 comes from.

]]>0.5 ln x=ln (x^0.5)

]]>[Edit: the integral symbols that I pasted from the row above came through as ?, so that will have to do. all the ? below are intended to be integral symbols.]

Integrate (x) = ln(x) / x on the interval [1, 100].

So I go like this:

u = ln(x)

du = 1/x dx

?(u * du) = ln(x)dx ? ln|x|dx = u² ... what?

I'm stuck; I don't get it. The solution in the book goes like this:

? [b=ln100, a=ln1] udu ->

u² | ln100

2 | ln1 ->

(ln100)² / 2 - 0

I understand why the limits of integration changed from [1, 100] to [ln1, ln100], and that the final expression is g(b) - g(a), which as I understand it is the final step to definite integration.

What I don't understand is, where did the /2 come from?

Thanks for the help. I hope my explanation is clear; some notation really doesn't translate to the web at all.

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