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Category: Integration

0-e-2arctg-t-2-dt-

Question Number 143622 by ArielVyny last updated on 16/Jun/21 $$\int_{\mathrm{0}} ^{\propto} {e}^{\mathrm{2}{arctg}\left({t}^{\mathrm{2}} \right)} {dt} \\ $$ Answered by TheHoneyCat last updated on 17/Jun/21 $$\mathrm{arctan}\left({t}\right)\underset{{t}\rightarrow+\infty} {\rightarrow}\frac{\pi}{\mathrm{2}}>\mathrm{0}…

Use-the-reduction-formular-I-n-sin-n-x-dx-1-n-sin-n-1-x-cos-x-n-1-n-I-n-2-to-evaluate-I-n-sin-6-x-dx-

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…

Calculus-n-1-1-n-k-1-n-k-2-

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-143588

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-143570

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}…

Please-help-explain-how-to-solve-e-1-x-dx-

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…