Question Number 31101 by abdo imad last updated on 02/Mar/18 $${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:{t}^{\mathrm{2}} \:{e}^{−\mathrm{2}{t}^{\mathrm{2}} } {sin}\left(\mathrm{2}\left({x}−{t}\right)\right){dt}\:{calculate} \\ $$$${f}^{''} \:+\mathrm{4}{f}\:\:{then}\:{finf}\:{f}\left({x}\right). \\ $$ Terms of Service Privacy…
Question Number 96637 by 175 last updated on 03/Jun/20 Commented by bemath last updated on 03/Jun/20 $$\int\:\frac{\mathrm{ln}\left(\mathrm{x}^{\mathrm{a}} \right)}{\mathrm{x}}\:\mathrm{dx}\:=\:\mathrm{a}\int\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{dx} \\ $$$$\mathrm{let}\:\mathrm{u}\:=\:\mathrm{ln}\:\left(\mathrm{x}\right)\:\Rightarrow\:\mathrm{du}\:=\:\frac{\mathrm{dx}}{\mathrm{x}} \\ $$$$\Rightarrow\mathrm{a}\int\:\mathrm{u}\:\mathrm{du}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}\:\mathrm{u}^{\mathrm{2}} +\mathrm{c}\: \\ $$$$=\:\frac{\mathrm{a}}{\mathrm{2}}\:\left(\mathrm{ln}\left(\mathrm{x}\right)\right)^{\mathrm{2}}…
Question Number 162174 by mnjuly1970 last updated on 27/Dec/21 $$ \\ $$$$\:\:\:\:{x}^{\:\mathrm{2}} −\:\mathrm{4}{x}\:−\mathrm{1}=\mathrm{0}\:\: \\ $$$$\:\:\:\:\:\alpha\:,\:\beta\:\:{are}\:{roots}\: \\ $$$$\:\:\:\:\:\alpha^{\:\mathrm{3}} \:+\:\mathrm{17}\beta\:+\mathrm{5}\:=? \\ $$$$\:\:−−−{solution}−−− \\ $$$$\:\:\:\alpha\:\:\:{is}\:{root}\:\:\:\Rightarrow\:\alpha^{\:\mathrm{2}} −\mathrm{4}\alpha\:−\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\Rightarrow\:\alpha^{\:\mathrm{2}}…
Question Number 31100 by abdo imad last updated on 02/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cosx}\:−{cos}\left(\mathrm{3}{x}\right)}{{x}}\:{e}^{−\mathrm{2}{x}} {dx}. \\ $$ Commented by abdo imad last updated on 04/Mar/18 $${let}\:{introduce}\:{the}\:{function}\:{f}\left({t}\right)=\int_{\mathrm{0}}…
Question Number 31098 by abdo imad last updated on 02/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{1}} ^{\infty} \:\:\frac{{arctan}\left({x}+\mathrm{1}\right)\:−{arctanx}}{{x}^{\mathrm{2}} }{dx}. \\ $$ Commented by abdo imad last updated on 04/Mar/18 $${let}\:{put}\:{I}\left(\xi\right)=\:\int_{\mathrm{1}}…
Question Number 31097 by abdo imad last updated on 02/Mar/18 $${calculate}\:{interms}\:{of}\:{a}\:{and}\:{b}\:{the}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({bt}\right)\:−{arctan}\left({at}\right)}{{t}}{dt}\:\:{with}\:{a}\:{and}\:{b}>\mathrm{0}. \\ $$ Commented by abdo imad last updated on 05/Mar/18…
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Question Number 31096 by abdo imad last updated on 02/Mar/18 $${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\left({a}+{bcosx}\right)^{\mathrm{2}} }\:{with}\:{a}>{b}>\mathrm{0}\:{then}\:{give}\:{the} \\ $$$${value}\:{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\left(\mathrm{2}+{cosx}\right)^{\mathrm{2}} } \\ $$ Commented by abdo imad…
Question Number 31094 by abdo imad last updated on 02/Mar/18 $${m}\:{and}\:{n}\:{integrs}\:{and}\:{y}\geqslant\mathrm{0}\:{find}\:\int_{\mathrm{0}} ^{{y}} \:{x}^{{m}} \left({y}−{x}\right)^{{n}} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31095 by abdo imad last updated on 02/Mar/18 $${find}\:{I}_{{n}} \left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:{t}^{{n}} \:{e}^{−{xt}} {dt}\:\:\:\:{x}>\mathrm{0}\:{n}\in\:{N}. \\ $$ Commented by abdo imad last updated on…