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BeMath-0-1-x-1-x-1-ln-x-dx-




Question Number 107695 by bemath last updated on 12/Aug/20
   ♠BeMath♠  ∫_0 ^1  ((x−1)/((x+1)ln x)) dx ?
$$\:\:\:\spadesuit\mathcal{B}{e}\mathcal{M}{ath}\spadesuit \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:{x}}\:{dx}\:?\: \\ $$
Answered by mnjuly1970 last updated on 12/Aug/20
ans:=ln((2/π))   tools:1.feynman′s trick  2.digamma function.
$${ans}:={ln}\left(\frac{\mathrm{2}}{\pi}\right)\: \\ $$$${tools}:\mathrm{1}.{feynman}'{s}\:{trick} \\ $$$$\mathrm{2}.{digamma}\:{function}. \\ $$
Commented by bemath last updated on 12/Aug/20
thanks
$${thanks} \\ $$

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