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Question Number 133471 by Abdoulaye last updated on 22/Feb/21

hos calcul ∫((lnx)/(x^2_  +1))dx ?

$${hos}\:{calcul}\:\int\frac{{lnx}}{{x}^{\mathrm{2}_{} } +\mathrm{1}}{dx}\:? \\ $$

Commented by Dwaipayan Shikari last updated on 22/Feb/21

For General ∫_0 ^∞ ((log(x))/(x^n +1))dx=−(π^2 /n^2 )cosec((π/n))cot((π/n))

$${For}\:{General}\:\int_{\mathrm{0}} ^{\infty} \frac{{log}\left({x}\right)}{{x}^{{n}} +\mathrm{1}}{dx}=−\frac{\pi^{\mathrm{2}} }{{n}^{\mathrm{2}} }{cosec}\left(\frac{\pi}{{n}}\right){cot}\left(\frac{\pi}{{n}}\right) \\ $$

Commented by Abdoulaye last updated on 22/Feb/21

how wi calcule??

$${how}\:{wi}\:{calcule}?? \\ $$

Commented by Abdoulaye last updated on 22/Feb/21

how do we calculate?

$${how}\:{do}\:{we}\:{calculate}? \\ $$

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