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Category: Integration

let-f-x-x-2-ln-1-x-3-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-3-calculate-f-x-dx-

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…

I-n-0-1-1-u-ud-u-Demonstrate-that-n-N-I-n-1-I-n-1-u-n-u-3-2-d-u-and-deduce-the-meaning-of-variations-of-I-n-N-

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…

find-thevalue-of-0-dx-1-x-6-by-using-the-value-of-dx-x-z-with-z-C-and-Im-z-0-

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…

1-decompose-inside-C-x-the-fraction-F-x-3-4-x-4-2-find-dx-x-z-with-z-from-C-3-find-the-value-of-3dx-4-x-4-

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}} }\:.…