Question Number 119934 by bramlexs22 last updated on 28/Oct/20 $$\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{8}} {x}−\mathrm{cos}\:^{\mathrm{8}} {x}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\:{dx}\: \\ $$ Answered by bobhans last updated on 28/Oct/20 $$\:\int\:\frac{\left(\mathrm{sin}\:^{\mathrm{4}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x}\right)\left(\mathrm{sin}\:^{\mathrm{4}}…
Question Number 119930 by Lordose last updated on 28/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{arcsin}\left(\mathrm{tan}\theta\right)\mathrm{d}\theta\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement} \\ $$$$\mathrm{arcsin}\left(\mathrm{tan}\theta\right)=\mathrm{x}\:\Rightarrow\mathrm{tan}\theta\:=\mathrm{sinx}\:\Rightarrow\theta\:=\mathrm{artan}\left(\mathrm{sinx}\right)\:\Rightarrow \\ $$$$\mathrm{A}\:=\int_{\mathrm{0}}…
Question Number 119920 by bramlexs22 last updated on 28/Oct/20 $$\:\int\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:=\:?\:,\:{x}\epsilon\left(−\mathrm{1},\mathrm{1}\right) \\ $$ Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{I}\:=\int\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\mathrm{dx}\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{cost}\:\Rightarrow \\ $$$$\mathrm{I}\:=\int\:\sqrt{\frac{\mathrm{2sin}^{\mathrm{2}} \left(\frac{\mathrm{t}}{\mathrm{2}}\right)}{\mathrm{2cos}^{\mathrm{2}}…
Question Number 185455 by cortano1 last updated on 22/Jan/23 $$\:\int\:\frac{{x}^{\mathrm{3}} .{e}^{{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$ Answered by SEKRET last updated on 22/Jan/23 $$\left.\:\:\mathrm{1}\right)\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}}…
Question Number 185451 by mathlove last updated on 22/Jan/23 Commented by Frix last updated on 22/Jan/23 $$\mathrm{Yes}. \\ $$ Commented by mathlove last updated on…
Question Number 54376 by Abdo msup. last updated on 02/Feb/19 $$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{ax}\:\:+\mathrm{1}} \\ $$$${with}\:\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{x}}{\left({x}^{\mathrm{2}} \:+{ax}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){find}\:{values}\:{of}\:{integrals}\:\int_{−\infty} ^{+\infty}…
Question Number 54374 by maxmathsup by imad last updated on 02/Feb/19 $${calculate}\:{h}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({at}\right)}{{ch}\left(\frac{{t}}{\mathrm{2}}\right)}{dt}\:. \\ $$ Commented by Abdo msup. last updated on 08/Feb/19 $${h}\left({a}\right)=_{\frac{{t}}{\mathrm{2}}={x}}…
Question Number 54372 by maxmathsup by imad last updated on 02/Feb/19 $${let}\:\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{{x}+{sint}}{dt}\:\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left({x}+{sint}\right)^{\mathrm{2}} }\:{dt}\: \\ $$$$\left.\mathrm{3}\right)\:{calculste}\:{for}\:{n}\in{N}\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sint}}{\left({x}+{sint}\right)^{{n}}…
Question Number 54371 by maxmathsup by imad last updated on 02/Feb/19 $${prove}\:{that}\:{ln}\left({z}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{z}−\mathrm{1}}{\mathrm{1}+{t}\left({z}−\mathrm{1}\right)}{dt}\:. \\ $$ Commented by maxmathsup by imad last updated on 02/Feb/19…
Question Number 54367 by maxmathsup by imad last updated on 02/Feb/19 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left[{t}\right]}{{t}}\:{t}^{−{p}} {dt}\:{interms}\:{of}\:\xi\left({p}\right)\:{with}\:{p}>\mathrm{0}\:. \\ $$ Commented by maxmathsup by imad last updated on…