Finding a definite integral from the Riemann sum

[crememars]

Homework Statement

Consider the following limit of a Riemann sum for a function f on [a, b]. Identify f, a, and b,
and express the limit as a definite integral.

*see actual expression in the description below. it was too complicated to type out so I included a picture instead.

Relevant Equations

∆x = (b-a)/n
xiR = a + i∆x

Hi! I am having trouble finalizing this problem.

The interval is given so we know that a = 1 and b = 2. From there you can figure out that ∆x = 1/n, xiR = 1 + i/n.
Using logarithmic properties, I rearranged the expression and wrote (1 + i/n)(1/n)ln[(n + i)/n].
I can guess that the function is going to look something like this: f(x) = xln(...) but I don't know what goes in the logarithmic function...

I have been trying to rewrite it in terms of xiR but no luck :(
any help would be really appreciated. thank you !

 

[pasmith]

Can you simplify the argument of the logarithm any further?

 

[crememars]

Can you simplify the argument of the logarithm any further?

Yes, I realized I was overcomplicating things. If I simplify (n+i)/n to (n/n +i/n) to (1+ i/n), I get f(x) = xlnx