Question Number 77758 by abdomathmax last updated on 09/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\sqrt{\mathrm{3}+{x}^{\mathrm{2}} }}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{2}}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77755 by abdomathmax last updated on 09/Jan/20 $$\left.\mathrm{1}\right){calculste}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} −{x}+{a}}}\:\:{with}\:\:{a}\:>\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral}\:{then}\:\:{find} \\ $$$${its}\:{value}. \\ $$$$ \\ $$$$ \\ $$ Commented…
Question Number 77752 by abdomathmax last updated on 09/Jan/20 $${let}\:{f}\left(\lambda\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{sin}\left(\:\lambda{e}^{{x}} \:+{e}^{−{x}} \right)}{{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} }{dx}\:{with}\:\lambda\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{detdrmine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left(\lambda\right)\:{at}\:{form}\:{ofintergral}\:{and}\:{find} \\ $$$${its}\:{value}. \\ $$…
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:…