A definite integral contianing ln(x) everyone, I met a tough definite integral as follows, I=int_1^oo(ln x)/((x+a)^m(x+b)^(n+1))dx, where a and b are constant, m and n are non-negative integers.

Zackary Diaz

Zackary Diaz

Answered question

2022-11-20

A definite integral contianing ln(x)
everyone, I met a tough definite integral as follows,
I = 1 ln x ( x + a ) m ( x + b ) n + 1 d x ,
where a and b are constant, m and n are non-negative integers.

Answer & Explanation

Sean Sutton

Sean Sutton

Beginner2022-11-21Added 17 answers

If   m , n N ,   then our integral can be expressed in terms of   J ( m 1 ,   n ) ( a , b ) ,   where J ( a , b ) =
= 1 ln x ( x + a ) ( x + b )   d x   =   0 0 1   =   ln 2 a ln 2 b 2 + Li 2 ( 1 a ) Li 2 ( 1 b ) a b ,

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