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Category: Integration

Find-the-cube-root-of-z-1-

Question Number 17392 by tawa tawa last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\:\mathrm{z}\:=\:−\:\mathrm{1} \\ $$ Answered by mrW1 last updated on 05/Jul/17 $$−\mathrm{1} \\ $$$$−\omega=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i} \\ $$$$−\omega^{\mathrm{2}}…

cos-x-2-cos-x-dx-

Question Number 17377 by tawa tawa last updated on 04/Jul/17 $$\int\:\:\frac{\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{2}\:−\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 05/Jul/17 $$\mathrm{cos}\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\left(\mathrm{x}/\mathrm{2}\right)}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{x}/\mathrm{2}\right)}\:=\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{t}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }…

k-1-m-1-n-n-m-1-nk-m-1-nk-m-

Question Number 148441 by qaz last updated on 28/Jul/21 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{m}−\mathrm{1}\right)}{\left(\mathrm{nk}+\mathrm{m}−\mathrm{1}\right)\left(\mathrm{nk}+\mathrm{m}\right)}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

1-1-x-4-dx-

Question Number 82891 by jagoll last updated on 25/Feb/20 $$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$ Answered by mind is power last updated on 25/Feb/20 $$\frac{\mathrm{1}}{.\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}=\underset{{n}\geqslant\:\mathrm{0}} {\sum}\frac{\left(\mathrm{2}{n}\right)!{t}^{\mathrm{2}{n}}…

1-find-W-xdx-a-2-x-2-y-2-with-W-a-x-2-y-2-a-2-and-x-gt-0-a-gt-0-2-calculate-W-1-xdx-x-2-y-2-1-

Question Number 82872 by abdomathmax last updated on 25/Feb/20 $$\left.\mathrm{1}\right){find}\:\int\int_{{W}} \:\frac{{xdx}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:{with} \\ $$$${W}_{{a}} \rightarrow{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant{a}^{\mathrm{2}} \:{and}\:{x}>\mathrm{0}\:\:\:\:\:\left({a}>\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int\int_{{W}_{\mathrm{1}} } \:\:\:\frac{{xdx}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…

1-sin-3xsin-x-

Question Number 17317 by palash Jana last updated on 04/Jul/17 $$\int\mathrm{1}/\sqrt{\mathrm{sin}\:\mathrm{3}{x}\mathrm{sin}\:\left({x}−\alpha\right)} \\ $$ Commented by Arnab Maiti last updated on 04/Jul/17 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is}\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{sin}^{\mathrm{3}} \mathrm{x}\:\mathrm{sin}\left(\mathrm{x}−\alpha\right)}} \\ $$…