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Question-224510

Question Number 224510 by Rogerkeyter last updated on 15/Sep/25 Answered by maths2 last updated on 16/Sep/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}+\frac{{ln}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)}{\mathrm{1}−{x}}{dx} \\ $$$$=\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}}…

there-is-a-number-when-the-digits-of-the-number-are-suffled-randomly-a-new-number-is-generated-which-is-double-of-the-first-number-The-question-is-what-is-the-smallest-number-which-satisfies-the-rule

Question Number 224393 by fantastic last updated on 07/Sep/25 $${there}\:{is}\:{a}\:{number}\: \\ $$$${when}\:{the}\:{digits}\:{of}\:{the}\:{number} \\ $$$${are}\:{suffled}\:{randomly}\:{a}\:{new} \\ $$$${number}\:{is}\:{generated}\:{which} \\ $$$${is}\:{double}\:{of}\:{the}\:{first}\:{number} \\ $$$${The}\:{question}\:{is} \\ $$$${what}\:{is}\:{the}\:{smallest}\:{number} \\ $$$${which}\:{satisfies}\:{the}\:{rules}?? \\…

Q224176-Sir-can-this-be-solved-without-using-trigonometry-If-not-can-you-please-show-me-the-way-which-uses-trig-the-least-

Question Number 224382 by fantastic last updated on 06/Sep/25 $${Q}\mathrm{224176}. \\ $$$${Sir}\:{can}\:{this}\:{be}\:{solved}\:{without} \\ $$$${using}\:{trigonometry}?? \\ $$$${If}\:{not}\:{can}\:{you}\:{please}\:{show}\:{me} \\ $$$${the}\:{way}\:{which}\:{uses}\:{trig}.{the}\:{least}?? \\ $$ Commented by Frix last updated…

recently-I-read-a-nice-proof-to-the-following-problem-I-know-everybody-can-look-it-up-but-if-you-re-interested-in-learning-something-try-it-by-yourself-first-don-t-post-the-answer-you-found-on-the-www

Question Number 224330 by Ghisom_ last updated on 03/Sep/25 $$\mathrm{recently}\:\mathrm{I}\:\mathrm{read}\:\mathrm{a}\:\mathrm{nice}\:\mathrm{proof}\:\mathrm{to}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{problem} \\ $$$$\mathrm{I}\:\mathrm{know}\:\mathrm{everybody}\:\mathrm{can}\:\mathrm{look}\:\mathrm{it}\:\mathrm{up}\:\mathrm{but}\:\mathrm{if}\:\mathrm{you}'\mathrm{re} \\ $$$$\mathrm{interested}\:\mathrm{in}\:\mathrm{learning}\:\mathrm{something}\:\mathrm{try}\:\mathrm{it}\:\mathrm{by} \\ $$$$\mathrm{yourself}\:\mathrm{first} \\ $$$$\mathrm{don}'\mathrm{t}\:\mathrm{post}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{you}\:\mathrm{found}\:\mathrm{on}\:\mathrm{the} \\ $$$${www}\:\mathrm{but}\:\mathrm{post}\:\mathrm{your}\:\mathrm{thoughts}\:\mathrm{instead} \\ $$$$ \\…