How to calculate the integral I=\int_0^1\frac{x^n-1}{\ln(x)}dx

Rylan Sullivan

Rylan Sullivan

Answered question

2022-04-23

How to calculate the integral
I=01xn1ln(x)dx

Answer & Explanation

Gianna Travis

Gianna Travis

Beginner2022-04-24Added 11 answers

If we replace x with e-t we are left with:
I=0+ete(n+1)ttdt=log(n+1)
by Frullani's theorem.
alastrimsmnr

alastrimsmnr

Beginner2022-04-25Added 18 answers

Hint: (ax)=axlog(a)

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