Question Number 77751 by abdomathmax last updated on 09/Jan/20 $${calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({e}^{{x}} +{e}^{−{x}} \right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by msup trace by abdo last…
Question Number 12201 by Nayon last updated on 16/Apr/17 $$\int\frac{\mathrm{1}}{{sin}\left({x}\right)}{dx} \\ $$ Answered by ajfour last updated on 16/Apr/17 $${I}=\int\:\frac{\left(\mathrm{cosec}\:{x}\right)\left(\mathrm{cosec}\:{x}+\mathrm{cot}\:{x}\right)}{\mathrm{cosec}\:{x}+\mathrm{cot}\:{x}}{dx} \\ $$$${let}\:\:\mathrm{cosec}\:{x}+\mathrm{cot}\:{x}\:=\:{t} \\ $$$$\frac{{dt}}{{dx}}=\:−\left(\mathrm{cosec}\:{x}\right)\mathrm{cot}\:{x}−\mathrm{cosec}\:^{\mathrm{2}} {x}…
Question Number 77729 by aliesam last updated on 09/Jan/20 $${prove}\:{that} \\ $$$$\int_{−\pi} ^{\pi} {cos}\left(\mathrm{2}{x}\right)\:{cos}\left(\mathrm{3}{x}\right)\:{cos}\left(\mathrm{4}{x}\right)….{cos}\left(\mathrm{2005}{x}\right){dx}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77716 by aliesam last updated on 09/Jan/20 $$\int{sin}\left({x}^{\mathrm{4}} \right)\:{dx} \\ $$ Commented by MJS last updated on 09/Jan/20 $$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{using}\:\mathrm{the}\:\mathrm{incomplete} \\ $$$$\mathrm{gamma}\:\mathrm{function}.\:\mathrm{I}'\mathrm{ll}\:\mathrm{post}\:\mathrm{it}\:\mathrm{later} \\ $$…
Question Number 143248 by cesarL last updated on 11/Jun/21 $$\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}} \\ $$ Commented by mohammad17 last updated on 11/Jun/21 $$ \\ $$$$=\int\:\frac{{dx}}{\left({x}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}}\int\:\frac{−{dx}}{\mathrm{1}−\left(\frac{{x}−\mathrm{2}}{\:\sqrt{\mathrm{3}}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}{coth}^{−\mathrm{1}}…
Question Number 143230 by qaz last updated on 11/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{x}^{\mathrm{3n}+\mathrm{1}} }{\mathrm{3n}+\mathrm{1}}=? \\ $$ Answered by mathmax by abdo last updated on 11/Jun/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sum_{\mathrm{n}=\mathrm{o}}…
Question Number 143219 by rs4089 last updated on 11/Jun/21 Commented by rs4089 last updated on 11/Jun/21 $${help}\:{me}\:{pleace} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 12141 by tawa last updated on 14/Apr/17 $$\int\:\mathrm{sin}\left(\mathrm{x}^{\mathrm{4}} \right)\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx} \\ $$ Answered by geovane10math last updated on 15/Apr/17 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know},\:\mathrm{put}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{Wolfram}\:\mathrm{Alpha}. \\…
Question Number 12139 by tawa last updated on 14/Apr/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:\mathrm{the}\:\mathrm{graphs}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{10x} \\ $$$$\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:−\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x} \\ $$ Answered by mrW1 last updated on 15/Apr/17 $$\mathrm{3}{x}^{\mathrm{3}}…
Question Number 77675 by TawaTawa last updated on 08/Jan/20 $$\int_{\:\mathrm{0}} ^{\:\:\infty} \:\mathrm{3}\left(\mathrm{2x}\:−\:\frac{\mathrm{3}}{\mathrm{x}}\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$ Answered by mind is power last updated on 09/Jan/20 $$\mathrm{diverge}\:…