Question Number 32363 by prof Abdo imad last updated on 23/Mar/18 $${let}\:{consider}\:{the}\:{function} \\ $$$${f}\left({x},\theta\right)\:=\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } {ln}\left(\:\mathrm{2}+{sin}\theta\:{cost}\right){dt} \\ $$$${calculate}\:\frac{\partial{f}}{\partial{x}}\left({x},\theta\right)\:{and}\:\:\frac{\partial{f}}{\partial\theta}\left({x},\theta\right)\:. \\ $$ Commented by prof Abdo…
Question Number 32362 by prof Abdo imad last updated on 23/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{3}\right)\left(\mathrm{2}{x}+\mathrm{5}\right)}\:. \\ $$ Answered by Joel578 last updated on 24/Mar/18 $${I}\:=\:\int_{\mathrm{0}} ^{\infty}…
Question Number 32361 by prof Abdo imad last updated on 23/Mar/18 $${let}\:{give}\:{a}>\mathrm{0}\:{find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{x}} }{\:\sqrt{{x}+{a}}}\:{dx}. \\ $$ Commented by abdo imad last updated on 25/Mar/18…
Question Number 32359 by prof Abdo imad last updated on 23/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)}\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 32360 by prof Abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{3}\right)}\:. \\ $$ Commented by abdo imad last updated on 25/Mar/18 $${I}\:=\:\int_{\mathrm{0}}…
Question Number 97892 by pranesh last updated on 10/Jun/20 Answered by john santu last updated on 10/Jun/20 $$\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4x} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4x} \\…
Question Number 32354 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{sin}^{\mathrm{2}} {t}\right)^{\mathrm{2}} }\:. \\ $$ Commented by abdo imad last updated on 28/Mar/18…
Question Number 32352 by abdo imad last updated on 23/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right){dx} \\ $$ Commented by abdo imad last updated on 26/Mar/18 $${ch}.{x}={sint}\:\Rightarrow\:{I}\:=\:\int_{\mathrm{0}}…
Question Number 32353 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}\left({x}\right){ln}\left({cos}\left({x}\right)\right){dx}\:. \\ $$ Answered by sma3l2996 last updated on 25/Mar/18 $${A}=\int_{\mathrm{0}} ^{\pi/\mathrm{4}} {cos}\left({x}\right){ln}\left({cosx}\right){dx}…
Question Number 32350 by abdo imad last updated on 23/Mar/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com