Question Number 78163 by TawaTawa last updated on 14/Jan/20 $$\int\:\sqrt{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{sin}\left(\theta\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\:\:\mathrm{d}\theta \\ $$ Commented by MJS last updated on 15/Jan/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$ Commented by…
Question Number 78134 by msup trace by abdo last updated on 14/Jan/20 $${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left(\mathrm{3}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 78135 by msup trace by abdo last updated on 14/Jan/20 $${explicit}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({xt}\right)}{{t}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dt} \\ $$$${with}\:{x}>\mathrm{0} \\ $$ Terms of Service Privacy…
Question Number 143638 by mnjuly1970 last updated on 16/Jun/21 $$\:\:\:\:\:\:\:\:\:\:……{Calculus}…. \\ $$$$\boldsymbol{\phi}:\overset{?} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right){ln}\left({x}\right)\left({ln}\left(\frac{\mathrm{1}−{x}}{{x}}\right)\right)}{{x}}\:{dx} \\ $$$$\:\:{m}.{n}…. \\ $$$$ \\ $$ Commented by TheHoneyCat last…
Question Number 143628 by ArielVyny last updated on 16/Jun/21 $$\int_{{x}} ^{\propto} {t}^{\alpha−\mathrm{1}} {e}^{{it}} {dt}=?? \\ $$ Answered by mathmax by abdo last updated on 16/Jun/21…
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 $$\mathrm{arctan}\left({t}\right)\underset{{t}\rightarrow+\infty} {\rightarrow}\frac{\pi}{\mathrm{2}}>\mathrm{0}…
Question Number 12533 by tawa last updated on 24/Apr/17 $$\mathrm{compute} \\ $$$$\int\mathrm{sec}^{\mathrm{5}} \left(\mathrm{x}\right)\:\mathrm{tan}^{\mathrm{3}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 25/Apr/17 $${I}=\int{sec}^{\mathrm{5}} \left({x}\right){tan}^{\mathrm{3}}…
Question Number 12535 by tawa last updated on 24/Apr/17 $$\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}}…