Evaluating: <msubsup> &#x222B;<!-- ∫ --> <mrow class="MJX-TeXAtom-ORD"> 1 </mro

lasquiyas5loaa

lasquiyas5loaa

Answered question

2022-05-12

Evaluating: 1 n [ ln ( x ) ln ( x ) ] d x
I am attempting to evaluate the integral:
1 n ln ( x ) ln ( x ) d x
To a form:
f ( x ) + O ( g ( x ) )
where g ( x ) 0 as x
How do I compute that f(x) or atleast some type of series representation for it?

Answer & Explanation

Oswaldo Rosales

Oswaldo Rosales

Beginner2022-05-13Added 16 answers

We have:
1 n ln ( x ) d x = ( x ln ( x ) x ) | 1 n = n ln ( n ) n + 1
And:
1 n ln ( x ) d x = i = 1 n 1 i i + 1 ln ( x ) d x = i = 1 n 1 i i + 1 ln ( i ) d x = i = 1 n 1 ln ( i ) = ln ( i = 1 n 1 i ) = ln ( ( n 1 ) ! )
Thus, your integral is equal to:
n ln ( n ) n + 1 ln ( ( n 1 ) ! )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?