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}}}…
Question Number 42370 by Raj Singh last updated on 24/Aug/18 Commented by maxmathsup by imad last updated on 24/Aug/18 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{{sin}\left(\mathrm{2}{x}\right)+{sinx}} \\ $$$${A}\:=\:\int\:\:\:\:\:\frac{{dx}}{\mathrm{2}{sinx}\:{cosx}\:+{sinx}}\:=\:\int\:\:\:\:\:\:\frac{{sinx}}{\mathrm{2}{sin}^{\mathrm{2}} {xcosx}\:+{sin}^{\mathrm{2}} {x}}\:{dx} \\…
Question Number 42374 by maxmathsup by imad last updated on 24/Aug/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:{arctan}\left({xt}^{\mathrm{2}} \right){cos}\left({t}^{\mathrm{2}} \right)\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:{cos}\left({t}^{\mathrm{2}}…
Question Number 42366 by Joel578 last updated on 24/Aug/18 $$\underset{\mathrm{2005}} {\overset{\mathrm{2017}} {\int}}\:\frac{\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2017}\mid\right)^{\mathrm{2017}} }{\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2015}\mid\right)^{\mathrm{2017}} \:+\:\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2017}\mid\right)^{\mathrm{2017}} }\:{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Aug/18 $$\int_{{a}}…