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 $$\mathrm{Put}\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{{e}^{{x}}…
Question Number 105440 by Ar Brandon last updated on 28/Jul/20 $$\int\mathrm{tanx}\centerdot\mathrm{tan2x}\centerdot\mathrm{tan3x}\centerdot\mathrm{dx} \\ $$$$\mathrm{Any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{without}\:\mathrm{the}\:\mathrm{use}\:\mathrm{of} \\ $$$$\mathrm{partial}\:\mathrm{fractions}? \\ $$ Commented by som(math1967) last updated on 29/Jul/20 $$\mathrm{tan3x}=\frac{\mathrm{tan2x}+\mathrm{tanx}}{\mathrm{1}−\mathrm{tan2xtanx}}…
Question Number 170953 by akolade last updated on 04/Jun/22 Commented by mokys last updated on 04/Jun/22 $$\frac{{xe}^{{x}\sqrt{{x}}} −{sin}^{\mathrm{5}} {x}\:{ln}^{\mathrm{7}} {x}}{\:\sqrt{{tanx}}−{arctan}^{\mathrm{3}} {x}}\:{t}\:+\:{c} \\ $$ Commented by…
Question Number 105412 by john santu last updated on 28/Jul/20 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right)\:{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 28/Jul/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…