Question Number 129230 by bramlexs22 last updated on 14/Jan/21 $$\:\mathrm{V}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{arctan}\:\left(\frac{\mathrm{x}}{\mathrm{y}}\right)\:\mathrm{dx}\:? \\ $$ Answered by bemath last updated on 14/Jan/21 Terms of Service Privacy…
Question Number 129228 by bramlexs22 last updated on 14/Jan/21 $$\:\mathrm{H}\:=\:\int\:\mathrm{tan}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{2x}\:\mathrm{tan}\:\mathrm{3x}\:\mathrm{dx}\:? \\ $$ Commented by som(math1967) last updated on 14/Jan/21 $${Q}\:\mathrm{105440} \\ $$ Terms of Service…
Question Number 129223 by bramlexs22 last updated on 14/Jan/21 $$\:\mathrm{W}\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{5x}+\mathrm{cos}\:\mathrm{4x}}{\mathrm{2cos}\:\mathrm{3x}−\mathrm{1}}\:\mathrm{dx}\: \\ $$ Answered by bobhans last updated on 14/Jan/21 $$\:{W}=\int\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{2cos}\:\mathrm{3}{x}−\mathrm{1}}\:{dx} \\ $$$$\:{W}=\int\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right).\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{2cos}\:\mathrm{3}{x}\mathrm{sin}\:\mathrm{3}{x}−\mathrm{sin}\:\mathrm{3}{x}}\:{dx} \\ $$$$\:{W}=\:\int\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{sin}\:\mathrm{6}{x}−\mathrm{sin}\:\mathrm{3}{x}}{dx} \\…
Question Number 129212 by bramlexs22 last updated on 13/Jan/21 $$\:\mathrm{M}\:=\:\int\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{5}}}\:\mathrm{dx}\:? \\ $$ Answered by TheSupreme last updated on 13/Jan/21 $${x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}={t} \\ $$ Answered…
Question Number 63667 by mathmax by abdo last updated on 07/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dt}}{{cost}\:+{x}\:{sint}}\:\:\:{wih}\:{x}\:{from}\:{R}. \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left({cost}\:+{xsint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\left[{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dt}}{{cos}\left(\mathrm{2}{t}\right)+\mathrm{2}{sin}\left(\mathrm{2}{t}\right)}\right. \\ $$…
Question Number 63666 by mathmax by abdo last updated on 07/Jul/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{dx}}{\mathrm{2}{sinx}\:+{cosx}} \\ $$ Commented by MJS last updated on 07/Jul/19 $$=\mathrm{0} \\…
Question Number 63664 by mathmax by abdo last updated on 07/Jul/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{{x}+{t}^{{n}} }\:{dt}\:\:\:{with}\:\mathrm{0}<{a}<\mathrm{1}\:\:{and}\:\:{x}>\mathrm{0}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\left({x}+{t}^{{n}} \right)^{\mathrm{2}} }\:{dt}…
Question Number 63661 by mathmax by abdo last updated on 06/Jul/19 $${let}\:\mathrm{0}<{a}<\mathrm{1}\:{find}\:{the}\:{valueof}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 63662 by mathmax by abdo last updated on 06/Jul/19 $$\:{let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{a}−\mathrm{1}} }{\mathrm{1}+{x}^{{n}} }{dx}\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2}\:\:{and}\:\mathrm{0}<{a}<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{{a}−\mathrm{1}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:{and}\:\int_{\mathrm{0}}…
Question Number 129180 by mnjuly1970 last updated on 13/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:{calculus}… \\ $$$$\:\:\:{calculate}:: \\ $$$$\:\:\:\:\:\:\phi\overset{???} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{dx}}{\left({sin}\left({x}\right)+{cos}\left({x}\right)+\sqrt{\mathrm{2}}\:\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by Dwaipayan…