Question Number 163469 by Zaynal last updated on 07/Jan/22 Commented by smallEinstein last updated on 07/Jan/22 Answered by amin96 last updated on 07/Jan/22 $$\Omega=−\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 97928 by M±th+et+s last updated on 10/Jun/20 $${find}\:{the}\:{general}\:{formula} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\alpha} \left({x}\right)\:{dx} \\ $$ Answered by abdomathmax last updated on 10/Jun/20 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 163467 by Zaynal last updated on 07/Jan/22 Answered by mr W last updated on 07/Jan/22 $${e}^{{x}} =\mathrm{1}+\frac{{x}}{\mathrm{1}!}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}…=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{\mathrm{2}{n}} }{\left(\mathrm{2}{n}\right)!}+\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 32367 by prof Abdo imad last updated on 23/Mar/18 $${let}\:\alpha\in{R}\:{and}\:{x}^{\mathrm{2}} \neq\mathrm{1}\:\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right){dt} \\ $$$${calculate}\:{f}\left({x}\right). \\ $$ Terms of Service…
Question Number 32365 by prof Abdo imad last updated on 23/Mar/18 $${let}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\:.{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{F}\left({x}\right)\:. \\ $$ Commented by prof Abdo imad last updated…
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}}…