Question Number 132070 by bramlexs22 last updated on 10/Feb/21 $$\mathrm{I}=\int\:\frac{\mathrm{x}}{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 10/Feb/21 $$\mathrm{I}=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} \right)}{\left(\left(\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}}…
Question Number 66520 by mhmd last updated on 16/Aug/19 $${find}\:{the}\:{length}\:{r}=\mathrm{2}/\mathrm{1}−{cos}\theta\:\:\:\:\:\:\:\:\:{if}\:\theta\:{between}\:{pi}/\mathrm{2}\:{to}\:{pi} \\ $$ Commented by kaivan.ahmadi last updated on 16/Aug/19 $${l}=\int_{\frac{\pi}{\mathrm{2}}} ^{\pi} \sqrt{\left(\frac{{dr}}{{d}\theta}\right)^{\mathrm{2}} +{r}^{\mathrm{2}} }{d}\theta \\…
Question Number 66517 by mhmd last updated on 16/Aug/19 $${find}\:{the}\:{area}\:{cos}\left(\mathrm{2}\theta\right) \\ $$ Commented by MJS last updated on 16/Aug/19 $$\mathrm{you}\:\mathrm{must}\:\mathrm{give}\:\mathrm{borders}… \\ $$ Answered by Smail…
Question Number 66502 by mhmd last updated on 16/Aug/19 $${find}\:{the}\:{area}\:{about}\:{cos}\left(\mathrm{2}\theta\right) \\ $$ Answered by mr W last updated on 16/Aug/19 $${A}=\mathrm{8}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{r}^{\mathrm{2}} {d}\theta}{\mathrm{2}} \\…
Question Number 949 by 123456 last updated on 04/May/15 $${f}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${f}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}{x}^{{n}} \mathrm{sin}\:{xdx} \\ $$$${g}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}{x}^{{n}} \mathrm{cos}\:{xdx} \\ $$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \\…
Question Number 132023 by mnjuly1970 last updated on 10/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:{calculus}….. \\ $$$${prove}\:{that}::: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left(\mathrm{2}{x}\right)}{{cosh}\left({x}\right)}\:{dx}\overset{?} {=}\frac{\pi}{\mathrm{2}{cosh}\left(\pi\right)} \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 66483 by ~ À ® @ 237 ~ last updated on 16/Aug/19 $$\:{calculate}\:\:\:\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\zeta\left({k}\right)\:\:\:\:\:\:\:{if}\:\:\:\:\zeta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{{n}^{{s}} }\: \\ $$ Commented by…
Question Number 945 by tera last updated on 04/May/15 $$\int_{\mathrm{1}} ^{\mathrm{2}} {x}^{\mathrm{2}} {sin}\mathrm{3}{x}\:{dx}\:=….. \\ $$ Answered by prakash jain last updated on 04/May/15 $$\mathrm{Integrate}\:\mathrm{by}\:\mathrm{parts} \\…
Question Number 66476 by aliesam last updated on 15/Aug/19 Commented by kaivan.ahmadi last updated on 15/Aug/19 $${t}=\mathrm{4}{x}+\mathrm{1}\Rightarrow \\ $$$$\frac{\left({t}−\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow\frac{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{t}}+\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow \\…
Question Number 943 by miguel last updated on 04/May/15 $${help}\:{me}.. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{lnx}}{\:\sqrt{\mathrm{1}−{x}}}{dx}=??? \\ $$$$ \\ $$ Commented by 123456 last updated on 04/May/15…