Question Number 139445 by aliibrahim1 last updated on 27/Apr/21 Answered by mr W last updated on 27/Apr/21 $${u}={xy} \\ $$$$\frac{{du}}{{dx}}={x}\frac{{dy}}{{dx}}+{y} \\ $$$$\frac{{du}}{{dx}}+\mathrm{3}{u}^{\mathrm{2}} =\mathrm{0} \\ $$$$−\frac{{du}}{{u}^{\mathrm{2}}…
Question Number 8375 by tawakalitu last updated on 09/Oct/16 $$\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$\mathrm{By}\:\mathrm{direct}\:\mathrm{integration}\:\mathrm{and}\:\mathrm{by}\:\mathrm{expanding} \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{power}\:\mathrm{series}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 8366 by tawakalitu last updated on 09/Oct/16 $$\int\frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{4}}}\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 139432 by normabaru last updated on 27/Apr/21 Answered by Jme Eduardo last updated on 27/Apr/21 $$\left({a}\right)\:\:{if}\:\:{x}={t}^{\mathrm{2}} \:\:{and}\:\:{y}={t} \\ $$$$ \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{2}{t}^{\mathrm{4}} }{{t}^{\mathrm{4}}…
Question Number 139429 by bemath last updated on 27/Apr/21 $$\int\:\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{12x}\right)\:\sqrt[{\mathrm{5}\:}]{\mathrm{cos}\:\mathrm{6x}}\:\mathrm{dx}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 139427 by Fikret last updated on 26/Apr/21 $$\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{3}\sqrt{\mathrm{2}}} {\int}}\sqrt{{x}^{\mathrm{2}} −\mathrm{2}}{dx}+\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}{dx}\:=? \\ $$ Answered by MJS_new last updated on 27/Apr/21…
Question Number 139402 by mathmax by abdo last updated on 26/Apr/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{log}^{\mathrm{2}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 8296 by tawakalitu last updated on 06/Oct/16 $$\mathrm{Give}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{representation}\:\mathrm{of}\:\:\mathrm{2333}! \\ $$ Commented by 123456 last updated on 07/Oct/16 $${n}!=\underset{\mathrm{0}} {\overset{+\infty} {\int}}{t}^{{n}} {e}^{−{t}} {dt} \\…
Question Number 73832 by FCB last updated on 16/Nov/19 Commented by FCB last updated on 16/Nov/19 $$\boldsymbol{\mathrm{solve}} \\ $$ Commented by MJS last updated on…
Question Number 8281 by tawakalitu last updated on 06/Oct/16 $$\int\frac{\mathrm{6}\:\mathrm{sinx}\:\mathrm{cosx}}{\mathrm{sinx}\:+\:\mathrm{cosx}}\:\mathrm{dx} \\ $$ Answered by Yozzias last updated on 06/Oct/16 $$\frac{\mathrm{sinx}}{\mathrm{sinx}+\mathrm{cosx}}=\mathrm{1}−\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}} \\ $$$$\therefore\:\mathrm{I}=\int\frac{\mathrm{sinxcosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\int\left(\mathrm{1}−\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\right)\mathrm{cosxdx} \\ $$$$=\int\left(\mathrm{cosx}−\frac{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}{\mathrm{sinx}+\mathrm{cosx}}\right)\mathrm{dx}…