Question Number 94510 by i jagooll last updated on 19/May/20 $$\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}\:{x}.\mathrm{cos}\:{x}}{dx}\: \\ $$ Commented by PRITHWISH SEN 2 last updated on 19/May/20 $$\int\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}.\sqrt{\mathrm{tanx}}}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:\:\mathrm{now}\:\mathrm{put}\:\mathrm{tanx}=\mathrm{t}^{\mathrm{2}} \\…
Question Number 28975 by abdo imad last updated on 02/Feb/18 $${find}\:{the}\:{value}\:{of}\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{7}} }{dx}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160013 by Odhiambojr last updated on 23/Nov/21 $$\int\frac{\mathrm{1}}{\mathrm{4}{sin}\:{x}+\mathrm{3}{cos}\:{x}}{dx} \\ $$$${evaluate} \\ $$ Commented by tounghoungko last updated on 23/Nov/21 $$\:\:{I}=\int\:\frac{{dx}}{\mathrm{4sin}\:{x}+\mathrm{3cos}\:{x}}\:=? \\ $$$$\mathrm{4sin}\:{x}+\mathrm{3cos}\:{x}=\mathrm{5}\left(\frac{\mathrm{4}}{\mathrm{5}}\mathrm{sin}\:{x}+\frac{\mathrm{3}}{\mathrm{5}}\mathrm{cos}\:{x}\right) \\…
Question Number 94432 by Tony Lin last updated on 18/May/20 $$\int\:\frac{{x}^{{n}} −{x}^{{n}−\mathrm{2}} }{\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}{C}_{{r}} ^{\mathrm{2}{n}} {x}^{{r}} }{dx}=? \\ $$$${The}\:{result}\:{is}\:{a}\:{little}\:{pretty} \\ $$ Commented by PRITHWISH…
Question Number 159960 by tounghoungko last updated on 23/Nov/21 $$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}\:=?\: \\ $$ Answered by MJS_new last updated on 23/Nov/21 $$\underset{\mathrm{0}}…
Question Number 28890 by abdo imad last updated on 31/Jan/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\:{x}\geqslant\mathrm{0}\:\:\:{x}\:−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\leqslant{ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{n}^{\mathrm{2}} }\right)^{{n}} . \\ $$ Terms of Service…
Question Number 28889 by abdo imad last updated on 31/Jan/18 $${find}\:\:{I}\:\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {ln}\left({x}−{e}^{{i}\theta} \right){d}\theta\:\:\:\:{and}\:{xfromR}\:{and}\:{x}^{\mathrm{2}} \neq\mathrm{1}. \\ $$ Commented by abdo imad last updated on 02/Feb/18…
Question Number 28886 by abdo imad last updated on 31/Jan/18 $${find}\:\int\:\:\:\frac{{x}}{{cos}^{\mathrm{2}} {x}}{dx}. \\ $$ Answered by mrW2 last updated on 01/Feb/18 $$\:\int\:\:\:\frac{{x}}{{cos}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int{x}\:{d}\left(\mathrm{tan}\:{x}\right)…
Question Number 28887 by abdo imad last updated on 31/Jan/18 $${find}\:\int\:\:{arcsin}\left(\sqrt{\frac{{x}}{{x}+\mathrm{2}}}\right){dx}. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{use}\:{the}\:{ch}.{arcsin}\left(\sqrt{\:\frac{{x}}{{x}+\mathrm{1}}}\:\right)={t}\:\Leftrightarrow\sqrt{\frac{{x}}{{x}+\mathrm{1}}}\:={sint} \\ $$$$\Leftrightarrow\frac{{x}}{{x}+\mathrm{1}}={sin}^{\mathrm{2}} {t}\:\Leftrightarrow{x}={xsin}^{\mathrm{2}}…
Question Number 28888 by abdo imad last updated on 31/Jan/18 $${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)}\:{with}\:{n}\in\:{N}^{\bigstar} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com