Question Number 152778 by mnjuly1970 last updated on 01/Sep/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Solve}\:………. \\ $$$$\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}.\:{sin}\left(\:{ln}\:\left({x}\:\right)\right){dx}\:\overset{?} {=}\:\frac{−\mathrm{1}}{\:\:\:\mathrm{5}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{solution}…. \\ $$$$\:\:\:\:\:\Omega\::\overset{{i}.{b}.{p}} {=}\left[\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{2}}\:.\:{sin}\left({ln}\left({x}\right)\right)\right]_{\mathrm{0}} ^{\:\mathrm{1}} −\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…
Question Number 21701 by Isse last updated on 01/Oct/17 $$\int\mathrm{2}{cot}^{\mathrm{2}} \mathrm{2}{t} \\ $$ Commented by Tikufly last updated on 01/Oct/17 $$\mathrm{I}\:\mathrm{think}\:\mathrm{your}\:\mathrm{question}\:\mathrm{should} \\ $$$$\mathrm{be}\:\int\mathrm{2cot}^{\mathrm{2}} \mathrm{2tdt} \\…
Question Number 21702 by Isse last updated on 01/Oct/17 $$\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \mathrm{1}/\mathrm{2}{cot}^{\mathrm{2}} \mathrm{2}\theta{d}\theta \\ $$ Commented by Tikufly last updated on 01/Oct/17 $$\int_{\pi/\mathrm{6}} ^{\pi/\mathrm{3}} \frac{\mathrm{1}}{\mathrm{2}{cot}^{\mathrm{2}}…
Question Number 21679 by Arnab Maiti last updated on 30/Sep/17 $$\int\frac{\mathrm{sec}\theta\:\mathrm{d}\theta}{\mathrm{1}−\mathrm{sec}\theta} \\ $$ Answered by alex041103 last updated on 30/Sep/17 $${First}\:{we}\:{make}\:{the}\:{following}\:{transformations}: \\ $$$$\int\frac{\mathrm{sec}\theta\:\mathrm{d}\theta}{\mathrm{1}−\mathrm{sec}\theta}=\int\frac{\frac{\mathrm{1}}{{cos}\theta}}{\mathrm{1}−\frac{\mathrm{1}}{{cos}\theta}}{d}\theta= \\ $$$$=\int\frac{\frac{\mathrm{1}}{{cos}\theta}}{\mathrm{1}−\frac{\mathrm{1}}{{cos}\theta}}\:\frac{{cos}\theta}{{cos}\theta}{d}\theta=…
Question Number 21680 by Arnab Maiti last updated on 30/Sep/17 $$\int\sqrt{\mathrm{sec}\theta}\:\mathrm{d}\theta \\ $$ Answered by alex041103 last updated on 30/Sep/17 $${First}: \\ $$$$\sqrt{{sec}\theta}=\sqrt{\frac{\mathrm{1}}{{cos}\theta}}=\frac{\mathrm{1}}{\:\sqrt{{cos}\theta}} \\ $$$${We}\:{know}\:{that}\:{cos}\left(\mathrm{2}\theta\right)=\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 152751 by talminator2856791 last updated on 01/Sep/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left(\mathrm{cos}\left(\mathrm{2cos}\left({x}\right)+\mathrm{1}\right)+\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{\left(\mathrm{ln}\left(\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}−{x}\right)\right)^{\mathrm{4}} }\:\:{dx} \\ $$$$\: \\ $$$$\: \\ $$…
Question Number 21662 by x² – y²@gmail.com last updated on 30/Sep/17 Answered by Joel577 last updated on 30/Sep/17 $${I}\:=\:\int\:\frac{\mathrm{8}{x}^{\mathrm{5}} \:−\:\mathrm{18}{x}^{\mathrm{3}} }{\mathrm{2}{x}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} }\:{dx}\:=\:\int\:\frac{\mathrm{2}{x}^{\mathrm{3}} \left(\mathrm{4}{x}^{\mathrm{2}} \:−\:\mathrm{9}\right)}{{x}^{\mathrm{2}}…
Question Number 152730 by puissant last updated on 31/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \frac{{tanx}}{\:\sqrt{\mathrm{2}{cosx}−\mathrm{1}}}{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 31/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{tan}{x}}{\:\sqrt{\mathrm{2cos}{x}−\mathrm{1}}} \\…
Question Number 152721 by SANOGO last updated on 31/Aug/21 Commented by SANOGO last updated on 31/Aug/21 $${ok}\:{merci}\:{bien}\:{mon}\:\:{prof}\:.{je}\:{m}'{excuse}\:{seulement}\:{je}\:{ne}\:{maitrise}\:{pas}\:{bien}\:{l}'{application}\:{c}'{est}\:{pourquoi} \\ $$ Commented by puissant last updated on…
Question Number 87185 by M±th+et£s last updated on 03/Apr/20 $$\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$ Answered by peter frank last updated on 03/Apr/20 $$\int\frac{\mathrm{2}{x}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx}−\int\frac{\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\…