Question Number 97059 by mhmd last updated on 06/Jun/20 Commented by PRITHWISH SEN 2 last updated on 06/Jun/20 $$\mathrm{let}\: \\ $$$$\:\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{sin}^{−\mathrm{1}} \mathrm{x}−\mathrm{1}}\:=\:\mathrm{v}\left(\mathrm{x}\right) \\ $$$$\mathrm{then}\:\mathrm{v}^{'}…
Question Number 97057 by bemath last updated on 06/Jun/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{−\mathrm{ln}\left({x}\right)}}\:?\:\left[\:{by}\:{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$ Answered by Sourav mridha last updated on 06/Jun/20 $$\boldsymbol{{let}}\:\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right)=−\boldsymbol{{k}}.. \\ $$$$=\int_{\mathrm{0}}…
Question Number 31517 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}}\:\:. \\ $$ Commented by abdo imad last updated on 12/Mar/18 $${let}\:{put}\:{I}\left(\xi\right)\:=\int_{−\mathrm{1}+\xi} ^{\mathrm{1}+\xi}…
Question Number 31516 by abdo imad last updated on 09/Mar/18 $${find}\:\int\:\:\:\frac{{dx}}{{x}\:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 16/Mar/18 $${I}\:=\:\int\:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:−{x}\right){dx}=\:\int\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:{dx}\:−\frac{{x}^{\mathrm{2}}…
Question Number 31515 by abdo imad last updated on 09/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{{chx}}\:. \\ $$ Commented by abdo imad last updated on 10/Mar/18 $${I}=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 31514 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }{dx}. \\ $$ Answered by sma3l2996 last updated on 10/Mar/18 $${by}\:{parts}\: \\…
Question Number 31512 by abdo imad last updated on 09/Mar/18 $${find}\:{lim}_{{x}\rightarrow\infty} \:\int_{{x}} ^{\mathrm{2}{x}} \:\:\frac{{cos}\left(\frac{\mathrm{1}}{{t}}\right)}{{t}}\:{dt}. \\ $$ Commented by abdo imad last updated on 12/Mar/18 $$\left.\exists\:{c}\:\in\right]{x},\mathrm{2}{x}\left[\:/\:\int_{{x}}…
Question Number 31513 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{2}\:+{cosx}}\:\:. \\ $$ Commented by abdo imad last updated on 10/Mar/18 $${the}\:{ch}.\:{e}^{{ix}} ={z}\:{give}…
Question Number 31506 by abdo imad last updated on 09/Mar/18 $${let}\:{f}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{sht}}{{t}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{f}\left({x}\right)\:. \\ $$ Commented by abdo imad…
Question Number 31507 by abdo imad last updated on 09/Mar/18 $${g}\:{is}\:{real}\:{function}\:{continue}\:{let} \\ $$$${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:{sin}\left({x}−{t}\right){g}\left({t}\right){dt} \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:{f}^{'} \left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} {cos}\left({t}−{x}\right){g}\left({t}\right){dt} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{f}\:{is}\:{so}<{ution}\:{of}\:{the}\:{diff}.{equa}. \\ $$$${y}^{''} \:+{y}\:={g}\left({x}\right)…