Question Number 96092 by mhmd last updated on 29/May/20 $${find}\:\int\frac{{dx}}{{tan}^{−\mathrm{1}} \left({x}\right)} \\ $$ Commented by bemath last updated on 30/May/20 $$\int\:\mathrm{cot}^{−\mathrm{1}} \left({x}\right)\:{dx}\:=\:\mathrm{I} \\ $$$$\mathrm{by}\:\mathrm{parts}\:.\:\mathrm{u}\:=\:\mathrm{cot}^{−\mathrm{1}} \left({x}\right)\Rightarrow{du}=−\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 30557 by abdo imad last updated on 23/Feb/18 $${if}\:\varphi\:{convexe}\:{and}\:{f}\:{continue}\:{on}\:\left[{a},{b}\right]\:{prove}\:{that} \\ $$$$\varphi\left(\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:{f}\left({t}\right){dt}\right)\leqslant\:\frac{\mathrm{1}}{{b}−{a}}\:\int_{{a}} ^{{b}} \:\varphi{of}\left({t}\right){dt}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30554 by abdo imad last updated on 23/Feb/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{xcos}\theta\:+\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{2}{xcos}\theta\:+\mathrm{1}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30555 by abdo imad last updated on 23/Feb/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{4}} }}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30548 by abdo imad last updated on 23/Feb/18 $${let}\:{put}\:\:{for}\:\mid\lambda\mid<\mathrm{1}\:\:\:\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{cos}\left({nx}\right)}{\mathrm{1}−\mathrm{2}\lambda{cosx}\:+\lambda^{\mathrm{2}} }{dx}\: \\ $$$${find}\:{u}_{{n}} \:{interms}\:{of}\:{n}\:{and}\:\lambda. \\ $$ Terms of Service Privacy Policy…
Question Number 30546 by abdo imad last updated on 23/Feb/18 $${find}\:{I}\:=\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{{x}^{\mathrm{2}} }{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96083 by john santu last updated on 29/May/20 $$\int\:\frac{\mathrm{e}^{\mathrm{x}} \left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$ Answered by john santu last updated on 29/May/20 $$\int\:\left(\frac{{e}^{{x}} }{\mathrm{1}+\mathrm{cos}\:{x}}\:+\:\frac{{e}^{{x}} \mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}\right){dx}\:=\:…
Question Number 30544 by abdo imad last updated on 23/Feb/18 $${find}\:{I}=\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{t}}{\mathrm{2}+{sint}}{dt}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96076 by bobhans last updated on 29/May/20 $$\int\:\mathrm{3x}.\mathrm{2}^{\mathrm{x}} \:\mathrm{dx}\:?\: \\ $$ Answered by i jagooll last updated on 29/May/20 $$\int\:\left(\mathrm{3x}\right)\:\mathrm{d}\left(\frac{\mathrm{2}^{\mathrm{x}} }{\mathrm{ln}\:\mathrm{2}}\right)\:=\: \\ $$$$\frac{\mathrm{3x}.\mathrm{2}^{\mathrm{x}}…
Question Number 30542 by abdo imad last updated on 23/Feb/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{{x}} \:\:{e}^{−{u}^{\mathrm{2}} } {du}=\:{x}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{e}^{−{x}^{\mathrm{2}} {tan}^{\mathrm{2}} {t}} }{{cos}^{\mathrm{2}} {t}}{dt}\:\:. \\ $$$$ \\ $$…