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hos-calcul-lnx-x-2-1-dx-




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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