Question Number 77790 by aliesam last updated on 10/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{−{log}\left({x}\right)}}\:{dx} \\ $$ Answered by MJS last updated on 10/Jan/20 $$\int\frac{{dx}}{\:\sqrt{−\mathrm{ln}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{−\mathrm{ln}\:{x}}\:\rightarrow\:{dx}=−\mathrm{2}{x}\sqrt{−\mathrm{ln}\:{x}}{dt}\right] \\…
Question Number 77778 by Dah Solu Tion last updated on 10/Jan/20 $$\int\frac{{cosx}}{\mathrm{2}−{cosx}}{dx} \\ $$$$ \\ $$ Commented by Tony Lin last updated on 10/Jan/20 $${let}\:{t}={tan}\frac{{x}}{\mathrm{2}},\:\frac{{dx}}{{dt}}=\frac{\mathrm{2}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 143312 by Ar Brandon last updated on 12/Jun/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{x}^{\mathrm{4}} }\mathrm{dx}=\frac{\pi}{\mathrm{3}} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\mathrm{1}\:\left(\mathrm{constant}\:\mathrm{function}\:\mathrm{unity}\right)…
Question Number 77757 by abdomathmax last updated on 09/Jan/20 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{\left({x}^{\mathrm{2}} −\mathrm{1}\right){dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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