Question Number 64649 by mathmax by abdo last updated on 20/Jul/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}\theta}{\mathrm{5}+\mathrm{3}{cos}\theta}{d}\theta \\ $$ Commented by mathmax by abdo last updated on 20/Jul/19…
Question Number 64642 by mmkkmm000m last updated on 19/Jul/19 $$\int\left({dx}\right)/{e}^{{x}} +{x} \\ $$ Commented by mathmax by abdo last updated on 20/Jul/19 $${let}\:{I}\:=\int\:\:\:\frac{{dx}}{{x}+{e}^{{x}} }\:\Rightarrow{I}\:=\int\:\:\:\frac{{e}^{−{x}} }{{xe}^{−{x}}…
Question Number 64635 by mathmax by abdo last updated on 19/Jul/19 $$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax…
Question Number 130167 by Lordose last updated on 23/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{ln}\left(\mathrm{u}\right)\mathrm{e}^{−\mathrm{u}} }{\left(\mathrm{1}+\mathrm{e}^{−\mathrm{u}} \right)^{\mathrm{2}} }\mathrm{du} \\ $$$$ \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 130158 by benjo_mathlover last updated on 23/Jan/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{segment}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{y}^{\mathrm{2}} \:=\:\:\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} \:\mathrm{if}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}=\:\:\:\mathrm{2}\:\mathrm{is}\:\mathrm{the}\:\mathrm{chord}\: \\ $$$$\mathrm{determining}\:\mathrm{the}\:\mathrm{segment}\: \\ $$ Answered by liberty last updated on…
Question Number 130149 by liberty last updated on 22/Jan/21 $$\:\Re\:=\:\int\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+…}}}}\:{dx} \\ $$$$\:\Im\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\ell\mathrm{n}\:{x}}{{x}+\mathrm{1}}\:{dx}\: \\ $$ Answered by MJS_new last updated on 22/Jan/21 $$\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+…}}}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{4}{x}+\mathrm{1}}}{\mathrm{2}} \\…
Question Number 130137 by mathmax by abdo last updated on 22/Jan/21 $$\mathrm{calculate}\:\mathrm{for}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{natural}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{n}} }\mathrm{dx}\:\:\:\left(\mathrm{n}\geqslant\mathrm{2}\right) \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 130132 by bait last updated on 22/Jan/21 $${solve}\:\int\int_{{G}} \left(\mathrm{7}{x}−{y}\right){dxdy},\:{where}\:{G}\:{is}\:{given}\:{by}\:{y}=\mathrm{0} \\ $$$${x}+\mathrm{2}{y}=\mathrm{3},\:{x}={y}^{\mathrm{2}} \\ $$$$ \\ $$$${i}\:{want}\:{to}\:{know}\:{if}\:{the}\:{integral}\:{below}\:{is}\:{a}\:{correct} \\ $$$${representation}\:{of}\:{the}\:{integral}\:{above}. \\ $$$$\:\left(\underset{\mathrm{0}} {\overset{\frac{\mathrm{3}}{\mathrm{2}}} {\int}}\underset{\mathrm{0}} {\overset{\frac{\mathrm{9}}{\mathrm{4}}} {\int}}\left(\mathrm{7}{x}−{y}\right){dxdy}\right).…
Question Number 130135 by mathmax by abdo last updated on 22/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{6}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 22/Jan/21…
Question Number 130133 by talminator2856791 last updated on 22/Jan/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{for}\:{x} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:{x}} \underset{{m}=\mathrm{0}} {\overset{\lceil{x}\rceil} {\sum}}{x}^{\mathrm{ln}\:{m}+\mathrm{1}} \:{dx}\:=\:{x}^{\mathrm{2}} \:,\: \\…