Log Integral 1

Calculus Level 4

$\large \int_0^1 \frac{x-1}{\ln(x)} \, dx = \ ?$

Give your answer to 3 decimal places.

1 solution

Dreizehn Dolmancé
Aug 17, 2015

Consider

$f(p)=\int _{ 0 }^{ 1 }{ \frac { { x }^{ p }-1 }{ log(x) } dx }$

Then

$f'(p)= \int _{ 0 }^{ 1 }{ { x }^{ p }dx } = \frac { 1 }{ p+1 }$

Then integrate.

$f(p)=ln(p+1) \rightarrow$

$f(1)=ln(2) \approx 0.693$

Can you please explain,how did you find $f'(p)$

Akhil Bansal - 5 years, 8 months ago