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Question Number 34605 by abdo mathsup 649 cc last updated on 08/May/18 $${decompose}\:{inside}\:{R}\left({x}\right)\:{thefraction} \\ $$$${F}\left({x}\right)=\:\:\frac{{x}^{\mathrm{5}} \:+\mathrm{1}}{{x}^{\mathrm{2}^{} } \left({x}−\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy…
Question Number 34596 by abdo mathsup 649 cc last updated on 08/May/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} =\left({n}+\mathrm{1}\right){H}_{{n}} \:−{n} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} ^{\mathrm{2}} \:\:=\left({n}+\mathrm{1}\right){H}_{{n}} ^{\mathrm{2}} \:\:−\left(\mathrm{3}{n}+\mathrm{1}\right){H}_{{n}}…
Question Number 100097 by Dwaipayan Shikari last updated on 24/Jun/20 $$\int\left({tanx}\right)^{{e}^{{i}\pi} } {dx} \\ $$ Commented by Dwaipayan Shikari last updated on 24/Jun/20 $$\int\left({tanx}\right)^{−\mathrm{1}} {dx}…
Question Number 34546 by Sudipmoi1999@ last updated on 07/May/18 $$\int\frac{{dx}}{{sinx}+{cosx}+{tanx}+{cosecx}+{secx}+{cotx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34500 by Neelam last updated on 07/May/18 $${prove} \\ $$$${t}\mathrm{an}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}{tan}\mathrm{2}{A}\right)+\mathrm{tan}^{−\mathrm{1}} \left({cotA}\right)+\mathrm{tan}^{−\mathrm{1}} \left({cot}^{\mathrm{3}} {A}\right)=\mathrm{0} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 07/May/18…
Question Number 165561 by LEKOUMA last updated on 03/Feb/22 $${I}=\int\frac{{dx}}{{x}^{\mathrm{8}} +{x}^{\mathrm{6}} } \\ $$$${J}=\int\frac{\mathrm{1}−{x}^{\mathrm{7}} }{{x}\left(\mathrm{1}+{x}^{\mathrm{7}} \right)}{dx} \\ $$$${Calculate}\:{I}\:{and}\:{J} \\ $$ Answered by MJS_new last updated…
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Question Number 100000 by Dwaipayan Shikari last updated on 24/Jun/20 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{32}}+\frac{\mathrm{1}}{\mathrm{243}}+\frac{\mathrm{1}}{\mathrm{1024}}+…\infty \\ $$ Commented by ajfour last updated on 27/Jun/20 $${this}\:{question}\:{number}\:{is}\:{a}\: \\ $$$${landmark},\:{congratulations} \\ $$$${to}\:{all}\:{of}\:{us}\:\:{related}\:{with}\:{this}\:…
Question Number 165528 by LEKOUMA last updated on 03/Feb/22 $$\int\frac{\mathrm{1}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$ Commented by mkam last updated on 03/Feb/22 $$=\:\int\:\frac{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:−{x}}{\left({x}+\mathrm{1}\right)}\:{dx}\:=\:\int\:\frac{\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}}}{\left({x}+\mathrm{1}\right)}\:−\:\frac{\left({x}+\mathrm{1}−\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)}\:{dx} \\ $$$$…