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1-prove-that-0-1-arctant-t-dt-0-1-lnt-1-t-2-dt-2-find-0-1-arctant-t-dt-at-form-of-serie-




Question Number 32731 by caravan msup abdo. last updated on 31/Mar/18
1) prove that  ∫_0 ^1  ((arctant)/t)dt=−∫_0 ^1   ((lnt)/(1+t^2 ))dt  2) find ∫_0 ^1  ((arctant)/t)dt at form of serie
$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctant}}{{t}}{dt}=−\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{lnt}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctant}}{{t}}{dt}\:{at}\:{form}\:{of}\:{serie} \\ $$

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