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Category: Integration

please-a-generall-Form-for-C-n-C-n-4-pi-2-k-1-n-1-k-1-2k-2n-2k-

Question Number 136325 by frc2crc last updated on 20/Mar/21 $${please}\:{a}\:{generall}\:{Form}\:{for}\:{C}\left({n}\right) \\ $$$${C}\left({n}\right)=\frac{\mathrm{4}}{\pi^{\mathrm{2}} }\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \zeta\left(\mathrm{2}{k}\right)\zeta\left(\mathrm{2}{n}−\mathrm{2}{k}\right) \\ $$ Commented by Dwaipayan Shikari last updated on…

Question-70784

Question Number 70784 by rajesh4661kumar@gmail.com last updated on 08/Oct/19 Commented by MJS last updated on 08/Oct/19 $$\mathrm{really}\:\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\sqrt{{x}+\mathrm{1}}}\:\mathrm{not}\:\frac{{x}+\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\right)\sqrt{{x}+\mathrm{1}}}? \\ $$ Commented by rajesh4661kumar@gmail.com last…

Question-136279

Question Number 136279 by aupo14 last updated on 20/Mar/21 Answered by mindispower last updated on 20/Mar/21 $$=\int{e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}+\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}={A} \\ $$$$\mathrm{2}{nd}\:{by}\:{part} \\ $$$$\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}}…

Question-136267

Question Number 136267 by Algoritm last updated on 20/Mar/21 Commented by liberty last updated on 20/Mar/21 $$\int_{{e}} ^{\:{e}^{\mathrm{2}} } \sqrt{{x}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{{x}+\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{x}+\frac{\mathrm{1}}{\mathrm{8}}\sqrt{…}}}}\:−\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{8}}\sqrt{…}}}}\:{dx} \\ $$ Terms of Service…

sin-101x-sin-99-x-dx-

Question Number 70719 by oyemi kemewari last updated on 07/Oct/19 $$\int\mathrm{sin}\:\left(\mathrm{101x}\right)\mathrm{sin}\:^{\mathrm{99}} \mathrm{x}\:\mathrm{dx} \\ $$ Answered by mind is power last updated on 07/Oct/19 $${sin}\left(\mathrm{101}{x}\right)={sin}\left(\mathrm{100}{x}\right){cos}\left({x}\right)+{sin}\left({x}\right){cos}\left(\mathrm{100}{x}\right) \\…