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Category: Integration

1-x-x-2-x-6-dx-

Question Number 172712 by ilhamQ last updated on 30/Jun/22 $$\mathrm{1}.\:\int\frac{{x}}{{x}^{\mathrm{2}} −{x}−\mathrm{6}}\:{dx}=… \\ $$ Answered by Ar Brandon last updated on 30/Jun/22 $$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{2}} −{x}−\mathrm{6}}{dx}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} −{x}−\mathrm{6}}{dx} \\…

Question-41634

Question Number 41634 by Tawa1 last updated on 10/Aug/18 Commented by maxmathsup by imad last updated on 10/Aug/18 $${I}\:\:=\:\int\:\:\:\:\frac{{dx}}{{sinx}\:+\frac{\mathrm{1}}{{cosx}}}\:=\:\:\int\:\:\:\:\:\:\frac{{cosx}}{{sinx}\:.{cosx}\:+\mathrm{1}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${I}\:=\:\int\:\:\:\:\:\:\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\frac{\mathrm{2}{t}\left(\mathrm{1}−{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}}…

Question-41627

Question Number 41627 by alex041103 last updated on 10/Aug/18 Commented by alex041103 last updated on 10/Aug/18 $${Just}\:{for}\:{fun}!\:{I}\:{have}\:{already}\:{posted} \\ $$$${this}\:{Q}.\:{around}\:{a}\:{year}\:{ago}.\:{The}\:{result} \\ $$$${is}\:{beautiful}\:{and}\:{worths}\:{giving}\:{it}\:{a}\:{try}. \\ $$$${Can}\:{you}\:{prove}\:{something}\:{interesting}. \\ $$$${Hint}:\:{Calculate}\:{the}\:{result}.…

Question-107162

Question Number 107162 by bobhans last updated on 09/Aug/20 Commented by Dwaipayan Shikari last updated on 09/Aug/20 $$\int_{−\mathrm{5}} ^{\mathrm{5}} \sqrt[{\mathrm{6}}]{\mathrm{5x}^{\mathrm{2}} +\mathrm{6}}\:\left(\mathrm{5x}−\mathrm{2}\right)\mathrm{dx}=\int_{−\mathrm{5}} ^{\mathrm{5}} \sqrt[{\mathrm{6}}]{\mathrm{5x}^{\mathrm{2}} +\mathrm{6}}\:\left(−\mathrm{5x}−\mathrm{2}\right)=\mathrm{I} \\…

Question-172653

Question Number 172653 by Mikenice last updated on 29/Jun/22 Answered by MJS_new last updated on 30/Jun/22 $$\int\frac{\left(−\mathrm{1}\right)^{\mathrm{1}/{x}} }{{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\pi\mathrm{i}}{{x}}\:\rightarrow\:{dx}=\frac{\mathrm{i}{x}^{\mathrm{2}} }{\pi}{dt}\right] \\ $$$$=−\int\frac{\mathrm{e}^{{t}} }{{t}}{dt}=−\mathrm{Ei}\:\left({t}\right)\:= \\…