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Question Number 183943 by SulaymonNorboyev last updated on 31/Dec/22

∫_(1−(√(πx))(d^(1/2) /dx^(1/2) )(1)) ^(Σ_(n=1) ^∞ (4/(4n^2 −1)) ) ((arctan(((2−x)/(1+2x))))/(x^2 −4x−1))dx

$$\int_{\mathrm{1}−\sqrt{\pi{x}}\frac{{d}^{\frac{\mathrm{1}}{\mathrm{2}}} }{{dx}^{\frac{\mathrm{1}}{\mathrm{2}}} }\left(\mathrm{1}\right)} ^{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{4}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:} \frac{\mathrm{arctan}\left(\frac{\mathrm{2}−{x}}{\mathrm{1}+\mathrm{2}{x}}\right)}{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{1}}{dx} \\ $$

Commented by SEKRET last updated on 02/Jan/23

sulaymon misolni tushuntirib yozing tepadagi suma 2 chiqadi integral olsa boladi bolaklab integral pastidagi nima eknaligini tushuntirib yozing qandaydir funksiyami yoki oddiy xarflarmi.

$$\:\:\boldsymbol{\mathrm{sulaymon}}\:\:\boldsymbol{\mathrm{misolni}}\:\:\boldsymbol{\mathrm{tushuntirib}}\:\:\boldsymbol{\mathrm{yozing}} \\ $$$$\boldsymbol{\mathrm{tepadagi}}\:\boldsymbol{\mathrm{suma}}\:\:\mathrm{2}\:\:\boldsymbol{\mathrm{chiqadi}}\:\:\boldsymbol{\mathrm{integral}}\:\:\boldsymbol{\mathrm{olsa}} \\ $$$$\boldsymbol{\mathrm{boladi}}\:\boldsymbol{\mathrm{bolaklab}}\:\:\boldsymbol{\mathrm{integral}}\:\:\boldsymbol{\mathrm{pastidagi}}\:\boldsymbol{\mathrm{nima}}\:\boldsymbol{\mathrm{eknaligini}} \\ $$$$\boldsymbol{\mathrm{tushuntirib}}\:\boldsymbol{\mathrm{yozing}}\:\:\boldsymbol{\mathrm{qandaydir}}\:\:\boldsymbol{\mathrm{funksiyami}} \\ $$$$\boldsymbol{\mathrm{yoki}}\:\:\boldsymbol{\mathrm{oddiy}}\:\:\boldsymbol{\mathrm{xarflarmi}}. \\ $$

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