Question Number 105565 by mathmax by abdo last updated on 30/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\mathrm{calculate}\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered…
Question Number 171096 by Kalebwizeman last updated on 07/Jun/22 $$ \\ $$$$\int\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:\:{please}\:{help} \\ $$ Answered by thfchristopher last updated on 07/Jun/22 $$\int\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 171090 by Kodjo last updated on 07/Jun/22 $${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)\sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} =\left(\mathrm{1}−{u}\right)^{{n}} {u}^{\frac{\mathrm{3}}{\mathrm{2}}} {d}\left({u}\right)\:\:{and}\:{deduce}\:{the}\:{meaning}\:{of}\:{variations}\:{of}\:\left({I}_{{n}} \right)\in{N} \\ $$ Commented by Kodjo…
Question Number 40007 by math khazana by abdo last updated on 15/Jul/18 $${find}\:{thevalue}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\mathrm{1}\:+{x}^{\mathrm{6}} }\:\:{by}\:{using}\:{the} \\ $$$${value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}−{z}}\:{with}\:{z}\:\in\:{C}\:{and}\:{Im}\left({z}\right)\neq\mathrm{0} \\ $$$$ \\ $$ Commented…
Question Number 40008 by math khazana by abdo last updated on 15/Jul/18 $$\left.\mathrm{1}\right)\:{find}\:\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}}\:\:+{x}\sqrt{{x}+\mathrm{1}}}\:. \\ $$ Commented by abdo mathsup 649 cc last updated on 15/Jul/18…
Question Number 171039 by Kodjo last updated on 06/Jun/22 $${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)^{{n}} \sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}} \geq\mathrm{0} \\ $$ Answered by thfchristopher last updated on…
Question Number 39967 by math khazana by abdo last updated on 14/Jul/18 $$\left.\mathrm{1}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\:\frac{\mathrm{3}}{\mathrm{4}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}−{z}}\:\:{with}\:{z}\:{from}\:{C} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{3}{dx}}{\mathrm{4}+{x}^{\mathrm{4}} }\:.…
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Question Number 105471 by Dwaipayan Shikari last updated on 29/Jul/20 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{{k}}\right)^{\mathrm{2}} \\ $$ Commented by Dwaipayan Shikari last updated on 29/Jul/20 $${What}\:{do}\:{you}\:{think}? \\…
Question Number 105455 by john santu last updated on 29/Jul/20 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{cos}\:{x}}\:{dx}\: \\ $$ Answered by 1549442205PVT last updated on 29/Jul/20 $$\mathrm{Put}\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{{e}^{{x}}…