how to find the integral of a rational logarithmic function I can't seem to figure this one out, i

George Bray

George Bray

Answered question

2022-06-21

how to find the integral of a rational logarithmic function
I can't seem to figure this one out,
it is:
ln ( x ) x d x
I substituted u for ln ( x ), so u = ln ( x ) and d u = 1 x d x
then to find x in terms of u: e u = x
so I get
u e u 2 d u
from here I can't figure out where to go, I have tried playing around with the numbers but after a few hours I figured I'd ask someone here.
I sense that I must somehow get it to the form
1 x d x ,
but i an not sure how to get a 1 in the numerator.

Answer & Explanation

Braylon Perez

Braylon Perez

Beginner2022-06-22Added 34 answers

Notice that 1 x is the derivation of log x so your integral has the form
f ( x ) f ( x ) d x
can you take it from here?
Micaela Simon

Micaela Simon

Beginner2022-06-23Added 3 answers

Your replacement of variables is wrong. Since u = ln x, you get
ln x 1 x d x
in which you replace ln x with u and 1 x d x with d u. What you get does not contain any e u or e u 2

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