Menu Close

Category: Integration

V-sin-x-sin-x-dx-

Question Number 129564 by bramlexs22 last updated on 16/Jan/21 $$\:\mathcal{V}\:=\:\int\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\left(\mathrm{x}+\theta\right)}\:\mathrm{dx}\: \\ $$ Answered by Lordose last updated on 16/Jan/21 $$\Omega\:=\:\int\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{sin}\left(\mathrm{x}+\theta\right)}\mathrm{dx}\:\overset{\mathrm{u}=\mathrm{x}+\theta} {=}\int\frac{\mathrm{sin}\left(\mathrm{u}−\theta\right)}{\mathrm{sin}\left(\mathrm{u}\right)}\mathrm{du} \\ $$$$\Omega\:=\:\int\frac{\mathrm{sin}\left(\mathrm{u}\right)\mathrm{cos}\theta−\mathrm{cos}\left(\mathrm{u}\right)\mathrm{sin}\theta}{\mathrm{sin}\left(\mathrm{u}\right)}\mathrm{du}\:=\:\mathrm{ucos}\theta\:−\:\mathrm{sin}\theta\mathrm{ln}\left(\mathrm{sinu}\right)\:+\:\mathrm{C} \\ $$$$\Omega\:=\:\left(\mathrm{x}+\theta\right)\mathrm{cos}\theta\:−\:\mathrm{sin}\theta\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{x}+\theta\right)\right)+\:\mathrm{C}…

modern-algebra-if-G-be-a-finite-group-and-O-G-pq-where-p-q-are-two-prime-numbers-p-gt-q-then-prove-that-G-has-

Question Number 129558 by mnjuly1970 last updated on 16/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{modern}\:\ast\ast\ast\ast\ast\ast\ast\ast\ast\ast\:{algebra}\:…\: \\ $$$$\:\:\:\:\:\:\:\::::\:\:{if}\:\:''\:{G}\:''\:{be}\:{a}\:{finite}\:{group}\:{and} \\ $$$$\:\:{O}\:\left({G}\right)={pq}\:\:,\:\:{where}\:''\:{p}\:,\:{q}\:''\:{are}\:{two} \\ $$$$\:\:{prime}\:\:{numbers}\:\left({p}\:>\:{q}\:\right)\:{then}\:{prove}\:{that}: \\ $$$$\:\:{G}\:\:{has}\:\:{at}\:{most}\:{one}\:{subgroup}\:{of}\:{order}\:''\:{p}\:''\:. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{written}\:{and}\:{compiled}\:{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit…. \\ $$ Answered…

cos-y-3-dy-

Question Number 129519 by BHOOPENDRA last updated on 16/Jan/21 $$\int\:{cos}\:\left({y}^{\mathrm{3}} \right){dy} \\ $$ Answered by Dwaipayan Shikari last updated on 16/Jan/21 $$\int{cos}\left({y}^{\mathrm{3}} \right){dy} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{e}^{{iy}^{\mathrm{3}}…

secxdx-

Question Number 63976 by Scientist0000001 last updated on 11/Jul/19 $$\int{secxdx}\:\:\:\:? \\ $$ Commented by Prithwish sen last updated on 12/Jul/19 $$\int\frac{\mathrm{sec}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \frac{\mathrm{x}}{\mathrm{2}}}\mathrm{dx}\:\:\:\:\mathrm{putting}\:\mathrm{tan}\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{t} \\ $$$$\mathrm{sec}^{\mathrm{2}}…

calculate-A-0-x-2017-1-x-2019-dx-and-B-0-x-2019-1-x-2021-dx-calculate-the-fraction-A-B-

Question Number 63892 by mathmax by abdo last updated on 10/Jul/19 $${calculate}\:{A}=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{2017}} }{\mathrm{1}+{x}^{\mathrm{2019}} }\:{dx}\:\:{and}\:{B}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{2019}} }{\mathrm{1}+{x}^{\mathrm{2021}} }\:{dx} \\ $$$${calculate}\:{the}\:{fraction}\:\frac{{A}}{{B}} \\ $$ Commented…

ln-x-ln-1-x-ln-1-2x-dx-

Question Number 63883 by mmkkmm000m last updated on 10/Jul/19 $$\int{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−\mathrm{2}{x}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 12/Jul/19 $${let}\:{A}\:=\int\:{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−\mathrm{2}{x}\right)\:{dx}\:\:{we}\:{have} \\ $$$${ln}^{'} \left(\mathrm{1}−{u}\right)\:=−\frac{\mathrm{1}}{\mathrm{1}−{u}}\:=−\sum_{{n}=\mathrm{0}}…