Question Number 162535 by mnjuly1970 last updated on 30/Dec/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\:\mathrm{ln}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{\:{x}^{\:\mathrm{4}} \:+\:\mathrm{17}{x}^{\:\mathrm{2}} \:+\:\mathrm{16}}\:{dx}\overset{?} {=}\:\frac{\pi}{\mathrm{60}}\:\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$ \\ $$ Commented by…
Question Number 31462 by abdo imad last updated on 08/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31463 by abdo imad last updated on 08/Mar/18 $${let}\:{give}\:{the}\:{function}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{1}−{cos}\theta\right){d}\theta \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{1}+{cos}\theta\right){d}\theta. \\ $$…
Question Number 31460 by abdo imad last updated on 08/Mar/18 $${find}\:{in}\:{terms}\:{of}\:\:{n}\:{the}\:{value}\:{of} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \left({x}^{\mathrm{2}} \:−\mathrm{2}{xcos}\left(\frac{{k}\pi}{{n}}\right)\:+\mathrm{1}\right){dx}\:\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$ Commented by abdo…
Question Number 31458 by abdo imad last updated on 08/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\sqrt{\mathrm{3}}} \:\:{arcsin}\left(\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right){dt}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31459 by abdo imad last updated on 08/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{cost}}{{cos}^{\mathrm{3}} {t}\:+{sin}^{\mathrm{3}} {t}}\:{dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 162525 by mathlove last updated on 30/Dec/21 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{\sqrt{{x}}}{\left({x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{4}\right)}=? \\ $$ Answered by Ar Brandon last updated on 24/Mar/22 $${I}=\int_{\mathrm{0}} ^{\infty}…
Question Number 96990 by Ar Brandon last updated on 06/Jun/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)^{\sqrt{\mathrm{x}}} \mathrm{dx} \\ $$ Answered by Sourav mridha last updated on 06/Jun/20 $$\int_{\mathrm{0}}…
Question Number 162512 by vishal1234 last updated on 30/Dec/21 $${solve}\:\int\sqrt{{cosec}^{\mathrm{2}} {x}−\mathrm{2}}\:{dx} \\ $$ Commented by MJS_new last updated on 30/Dec/21 $$\mathrm{2}\:\mathrm{steps}\:\mathrm{are}\:\mathrm{necessary} \\ $$$$\left(\mathrm{1}\right)\:{t}=\mathrm{cos}\:{x} \\ $$$$\left(\mathrm{2}\right)\:{u}=\sqrt{\mathrm{2}}{t}+\sqrt{\mathrm{2}{t}^{\mathrm{2}}…
Question Number 162513 by Lordose last updated on 30/Dec/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{log}\left(\mathrm{x}\right)}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{9}\right)} \\ $$ Answered by abdullahoudou last updated on 30/Dec/21 $${x}−>\frac{\mathrm{9}}{{x}} \\ $$ Answered…