Question Number 164672 by mathlove last updated on 20/Jan/22 Answered by Ar Brandon last updated on 20/Jan/22 $$\Omega=\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cos}{x}+\mathrm{1}}{\:\sqrt{\mathrm{3}+\mathrm{4cos}{x}+\mathrm{cos}^{\mathrm{2}} {x}}}{dx}=\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cos}{x}+\mathrm{1}}{\:\sqrt{\left(\mathrm{cos}{x}+\mathrm{1}\right)\left(\mathrm{cos}{x}+\mathrm{3}\right)}}{dx} \\ $$$$\:\:\:\:=\int_{\mathrm{0}}…
Question Number 33599 by abdo imad last updated on 19/Apr/18 $${calculatef}\left({a}\right)=\:\:\int_{−{a}} ^{{a}} \:\:\:\:\frac{{dx}}{\left({t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:\:{with}\:{a}>\mathrm{0}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 33590 by abdo imad last updated on 19/Apr/18 $${let}\:\alpha\:>\mathrm{1}\:\:{calculate}\:{f}\left(\alpha\right)\:=\:\int_{\alpha} ^{+\infty} \:\:\frac{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:. \\ $$ Commented by abdo imad last updated on…
Question Number 33589 by abdo imad last updated on 19/Apr/18 $$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\:\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{4}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} }\:. \\ $$ Commented by math khazana…
Question Number 33587 by abdo imad last updated on 19/Apr/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} {ln}\:\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\right){d}\theta\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${give}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99120 by M±th+et+s last updated on 18/Jun/20 $${prove}\:{that}: \\ $$$$\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\infty} {e}^{−\left(\mathrm{4}{x}^{\mathrm{6}} +\mathrm{12}{x}^{\mathrm{5}} +\mathrm{15}{x}^{\mathrm{4}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} +{x}\right)} {dx} \\ $$$$=\frac{\sqrt[{\mathrm{8}}]{{e}}}{\mathrm{3}}\left[\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{6}}\right)^{\frac{−\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{1}/\mathrm{3},\mathrm{2}/\mathrm{3}} ^{\mathrm{1}/\mathrm{6}} \mid\frac{−\mathrm{1}}{\mathrm{69}/\mathrm{2}}\:\right)\:+\frac{\Gamma\left(\mathrm{5}/\mathrm{6}\right)}{\mathrm{128}\sqrt[{\mathrm{3}}]{\mathrm{4}}}\mathrm{1}{F}\mathrm{2}\left(_{\mathrm{4}/\mathrm{3},\mathrm{5}/\mathrm{3}}…
Question Number 99114 by M±th+et+s last updated on 18/Jun/20 $${calculate}: \\ $$$$\int\sqrt{{x}}{sinh}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$${where}\:{sinh}^{−\mathrm{1}} \left({x}\right)\:{is}\:{the}\:{inverse}\:{hyperbolic}\: \\ $$$${sine}\:{function} \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 33570 by Joel578 last updated on 19/Apr/18 $${A}\:=\:\underset{{n}=\mathrm{2}} {\overset{\mathrm{2017}} {\sum}}\:\left[\underset{\mathrm{1}} {\overset{{n}} {\int}}\:\mathrm{2tan}^{−\mathrm{1}} \:{x}\:+\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:{dx}\right] \\ $$$${B}\:=\:\underset{{n}=\mathrm{2}} {\overset{\mathrm{2017}} {\prod}}\:\left[\underset{\mathrm{1}} {\overset{{n}} {\int}}\:\mathrm{2tan}^{−\mathrm{1}} \:{x}\:+\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}}…
Question Number 33544 by math khazana by abdo last updated on 19/Apr/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:{e}^{−{tx}^{\mathrm{2}} } }{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:{with}\:{t}\:>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 164605 by amin96 last updated on 19/Jan/22 Answered by Zaynal last updated on 19/Jan/22 $$\frac{\mathrm{In}\left(\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{2}}{\mathrm{12}} \\ $$ Terms of Service Privacy Policy…