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Question Number 107679 by seedhamaieng@gmail.com last updated on 12/Aug/20 $$\mathrm{dear}\:\mathrm{tinku}\:\mathrm{tara}\: \\ $$$$\mathrm{Please}\:\mathrm{add}\:\mathrm{a}\:\mathrm{option}\:\mathrm{which}\:\mathrm{gives}\: \\ $$$$\mathrm{us}\:\mathrm{to}\:\mathrm{save}\:\mathrm{a}\:\mathrm{file}\:\mathrm{as}\:\mathrm{pdf}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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Question-173188

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Question Number 173188 by dragan91 last updated on 08/Jul/22 Answered by mr W last updated on 08/Jul/22 $${t}=\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:>\mathrm{0} \\ $$$$\frac{\mathrm{2}{t}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}+\frac{\mathrm{2}\left({t}^{\mathrm{2}} +\mathrm{1}\right)}{{t}}=\mathrm{4}+\sqrt{\mathrm{2}} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{t}}}}+{t}+\frac{\mathrm{1}}{{t}}=\mathrm{2}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}…

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Question-107639

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Question Number 107639 by mathdave last updated on 11/Aug/20 Answered by mathmax by abdo last updated on 12/Aug/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{xln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx}\:\:\mathrm{we}\:\mathrm{have}\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}}\:=\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{\mathrm{n}} \:\mathrm{x}^{\mathrm{n}}…

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