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Author: Tinku Tara

Given-3xf-1-x-f-x-2x-2-and-f-3-f-9-f-a-three-first-term-in-AP-respectively-Find-the-value-of-a-

Question Number 128942 by bramlexs22 last updated on 11/Jan/21 $$\:\mathrm{Given}\::\:\mathrm{3}{xf}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\mathrm{2}{x}+\mathrm{2}\: \\ $$$${and}\:{f}\left(\mathrm{3}\right),\:\mathrm{f}\left(\mathrm{9}\right)\:,\:\mathrm{f}\left(\mathrm{a}\right)\:\mathrm{three}\:\mathrm{first} \\ $$$$\mathrm{term}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{respectively}.\:\mathrm{Find} \\ $$$$\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:?\: \\ $$ Answered by liberty last updated on 11/Jan/21…

1-find-x-1-x-3-3x-2-dx-2-calculate-4-x-1-x-3-3x-2-dx-

Question Number 63404 by mathmax by abdo last updated on 03/Jul/19 $$\left.\mathrm{1}\right)\:{find}\:\:\int\:\:\:\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}\:−\mathrm{2}}{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{4}} ^{+\infty} \:\:\:\:\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}\:+\mathrm{2}}{dx} \\ $$ Commented by MJS last updated…

let-f-t-0-ln-1-tx-1-x-2-dx-with-t-lt-1-1-determine-a-explicit-form-of-f-t-2-find-the-value-of-0-ln-1-x-1-x-2-dx-

Question Number 63395 by mathmax by abdo last updated on 03/Jul/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left(\mathrm{1}+{tx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:\:{with}\:\:\mid{t}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented…