Question Number 42435 by maxmathsup by imad last updated on 25/Aug/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\:\sqrt{{x}}\:+\sqrt{\mathrm{1}−{x}}} \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18…
Question Number 42430 by maxmathsup by imad last updated on 25/Aug/18 $${find}\:\int\:\:\:\:\:\:\:\frac{{dx}}{\mathrm{3}+{tan}^{\mathrm{2}} {x}} \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{\mathrm{3}+{tan}^{\mathrm{2}}…
Question Number 107965 by bemath last updated on 13/Aug/20 $$\:\:\:\:\frac{\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc}{} \\ $$$$\int\:{x}\:\sqrt{\frac{{x}}{\mathrm{2}{a}−{x}}}\:{dx}\:?\: \\ $$ Answered by bobhans last updated on 13/Aug/20 $$\:\:\frac{\ddots\mathscr{BOBHANS}\iddots}{\Pi} \\ $$$$\:\mathrm{I}=\:\int\:\mathrm{x}\:\sqrt{\frac{\mathrm{x}}{\mathrm{2a}−\mathrm{x}}}\:\mathrm{dx}\:\:\left[\:\mathrm{set}\:\mathrm{x}\:=\:\mathrm{a}−\mathrm{acos}\:\mathrm{2t}\:\right] \\…
Question Number 173486 by mnjuly1970 last updated on 12/Jul/22 $$ \\ $$$$\:\:\:\:\boldsymbol{\phi}\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\:\left({ax}\right)−\:{sin}\left({bx}\right)}{{x}^{\:\mathrm{2}} }{dx}\:\:=? \\ $$$$\:\:\: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−\mathrm{2}{sin}^{\:\mathrm{2}} \left(\frac{{ax}}{\mathrm{2}}\right)−\left(\mathrm{1}−\mathrm{2}{sin}^{\:\mathrm{2}} \left(\frac{{bx}}{\mathrm{2}}\right)\right)}{{x}\:^{\mathrm{2}} }{dx} \\…
Question Number 42407 by Tawa1 last updated on 25/Aug/18 $$\int\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tanx}}\:\mathrm{dx} \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18 $${let}\:{I}\:\:=\:\int\:\:\:\:\:\frac{{dx}}{\mathrm{1}+{tanx}}\:\:{changement}\:{tanx}\:={t}\:{give} \\ $$$${I}\:\:=\:\int\:\:\:\:\:\frac{\mathrm{1}}{\left(\mathrm{1}+{t}\right)\left({t}^{\mathrm{2}} \:+\mathrm{1}\right)}{dt}\:\:{let}\:{decompose}\:{F}\left({t}\right)\:=\:\:\frac{\mathrm{1}}{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{2}}…
Question Number 42402 by abdo.msup.com last updated on 24/Aug/18 $${calculate}\:\int\int_{{x}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 42395 by abdo.msup.com last updated on 24/Aug/18 $${calculate}\:\int\int_{{D}} \:\:\:\:\:\:\frac{{xy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:/\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1},\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$ Commented by maxmathsup by imad…
Question Number 42394 by abdo.msup.com last updated on 24/Aug/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{t}+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:{dt} \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18 $${changement}\:\:\:{t}\:=\:{sinx}\:{give}…
Question Number 42392 by abdo.msup.com last updated on 24/Aug/18 $${calculate}\:\int\:\:\:\frac{{lnx}}{{x}\:+{x}\left({lnx}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18 $${changement}\:{ln}\left({x}\right)\:={t}\:{give}\: \\ $$$${I}\:\:=\:\int\:\:\:\:\:\:\:\frac{{t}}{{e}^{{t}}…
Question Number 42391 by abdo.msup.com last updated on 24/Aug/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{tanx}\right){dx} \\ $$ Commented by maxmathsup by imad last updated on 25/Aug/18 $${let}\:{A}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…