Question Number 12535 by tawa last updated on 24/Apr/17 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{reduction}\:\mathrm{formular}. \\ $$$$\mathrm{I}_{\mathrm{n}} \:=\:\int\mathrm{sin}^{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx}\:=\:−\frac{\mathrm{1}}{\mathrm{n}}\:\mathrm{sin}^{\mathrm{n}\:−\:\mathrm{1}} \left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{x}\right)\:+\:\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\mathrm{I}_{\mathrm{n}} \:−\:\mathrm{2}\:,\:\mathrm{to}\:\mathrm{evaluate}\: \\ $$$$\mathrm{I}_{\mathrm{n}\:} =\:\int\mathrm{sin}^{\mathrm{6}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by mrW1…
Question Number 143603 by mnjuly1970 last updated on 16/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{k}} \left(\mathrm{1}+{n}\right)}\:\:\:\left({k}\geqslant\:\mathrm{2}\right)\:…… \\ $$ Answered by Dwaipayan Shikari last updated on 16/Jun/21…
Question Number 143588 by bobhans last updated on 16/Jun/21 Answered by EDWIN88 last updated on 16/Jun/21 $$\mathrm{F}\left(\mathrm{x}\right)=\underset{\mathrm{4}} {\overset{\mathrm{8x}} {\int}}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:=\:\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} }\:+\:\mathrm{c}\: \\ $$$$\mathrm{F}\:'\left(\mathrm{x}\right)=\:\mathrm{8f}\left(\mathrm{8x}\right)=\frac{\mathrm{x}}{\:\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} }}\: \\ $$$$\mathrm{F}'\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{8x}\right)=\frac{\mathrm{x}}{\mathrm{8}\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}}…
Question Number 143570 by cesarL last updated on 15/Jun/21 Answered by Ar Brandon last updated on 15/Jun/21 $$\mathrm{I}=\int\mathrm{tan}^{\mathrm{2}} \mathrm{8xsec}^{\mathrm{4}} \mathrm{8xdx} \\ $$$$\:\:=\int\mathrm{tan}^{\mathrm{2}} \mathrm{8xsec}^{\mathrm{2}} \mathrm{8x}\centerdot\mathrm{sec}^{\mathrm{2}} \mathrm{8xdx}…
Question Number 12500 by FilupS last updated on 24/Apr/17 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{explain}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\int{e}^{\frac{\mathrm{1}}{{x}}} {dx} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 24/Apr/17 $${e}^{\frac{\mathrm{1}}{{x}}} ={t}\Rightarrow\frac{\mathrm{1}}{{x}}={lnt}\Rightarrow\left({lnx}+{c}\right)^{'} ={lnt}\Rightarrow…
Question Number 143556 by Ar Brandon last updated on 15/Jun/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143545 by mathmax by abdo last updated on 15/Jun/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{6}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Answered by Pagnol last updated on 15/Jun/21 $$\mathrm{I}=\int_{\mathrm{0}}…
Question Number 78013 by jagoll last updated on 13/Jan/20 $${if}\::\:\mathrm{30}{x}^{\mathrm{4}} −\frac{\mathrm{15}}{\mathrm{8}}=\:\underset{{t}} {\overset{{x}} {\int}}\:{g}\left({u}\right){du} \\ $$$${find}\:{g}\left({t}\right). \\ $$ Answered by john santu last updated on 13/Jan/20…
Question Number 12463 by tawa last updated on 23/Apr/17 $$\int\:\:\frac{\mathrm{x}\:+\:\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:+\:\mathrm{3}\right)^{\mathrm{2}/\mathrm{3}} }\:\:\mathrm{dx} \\ $$ Answered by ridwan balatif last updated on 23/Apr/17 $$\int\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\right)^{\mathrm{2}} }}\mathrm{dx}…
Question Number 12464 by tawa last updated on 23/Apr/17 $$\int\:\mathrm{sin}^{\mathrm{3}} \left(\mathrm{7x}\right)\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 23/Apr/17 $$\mathrm{sin}\:\mathrm{3}{x}=\mathrm{3sin}\:{x}−\mathrm{4sin}\:^{\mathrm{3}} {x} \\ $$$${I}=\int\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{7}{x}\right){dx}…