Question Number 110543 by mnjuly1970 last updated on 29/Aug/20 Answered by mathdave last updated on 29/Aug/20 $${solution} \\ $$$${let}\:{y}={x}^{\mathrm{2}} \:\:{and}\:{dx}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{{y}}}{dy}\:\:{then}\:{putting}\:{into} \\ $$$${I}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}−{y}\right)\mathrm{ln}\left(\mathrm{1}+{y}\right)}{{y}}{dy} \\…
Question Number 44994 by manish09@gmail.com last updated on 07/Oct/18 $$\int\mathrm{e}^{\mathrm{x}} \left(\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}\right)\mathrm{dx}\:=\:? \\ $$ Answered by arvinddayama01@gmail.com last updated on 07/Oct/18 $$\mathrm{i}\:\mathrm{think}\:\mathrm{problem}\:\mathrm{should}\:\mathrm{be}:− \\ $$$$\:\:\:\:\:\:\int\mathrm{e}^{\mathrm{x}} \left(\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\mathrm{1}−\mathrm{cosx}}\right)\mathrm{dx} \\…
Question Number 44992 by manish09@gmail.com last updated on 07/Oct/18 $$\int\mathrm{e}^{\mathrm{x}} \left(\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right)\mathrm{dx}\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Oct/18 $$\int{e}^{{x}} \left(\frac{\mathrm{1}−\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}}{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}\right) \\ $$$$\int{e}^{{x}}…
Question Number 44993 by arvinddayama01@gmail.com last updated on 07/Oct/18 $$\int\frac{\mathrm{x}}{\mathrm{sin}\:\mathrm{x}}\mathrm{dx}=? \\ $$ Commented by maxmathsup by imad last updated on 07/Oct/18 $${let}\:{I}\:\left({t}\right)=\int_{\mathrm{0}} ^{{t}} \:\frac{{x}}{{sinx}}{dx}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={u}\:{give} \\…
Question Number 44921 by manish09@gmail.com last updated on 06/Oct/18 $$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{ln}\:\mathrm{x}}=? \\ $$ Commented by MJS last updated on 06/Oct/18 $$\mathrm{see}\:\mathrm{question}\:\mathrm{44674} \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 110450 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3y}^{\mathrm{2}} \right)\:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{3y}^{\mathrm{2}} } \:\mathrm{dxdy} \\ $$ Answered by mathmax by…
Question Number 110451 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\left[\frac{\mathrm{1}}{\mathrm{n}},\mathrm{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} } \mathrm{dxdy} \\ $$$$\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$…
Question Number 110448 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4i}\right)^{\mathrm{3}} }\mathrm{dx}\:\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$ Answered by mathmax by abdo last updated…
Question Number 110447 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{ix}\:+\mathrm{1}\right)^{\mathrm{2}} }\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$ Answered by mathmax by abdo last updated…
Question Number 175937 by qaz last updated on 09/Sep/22 $${if}\:{y}\left({x}−{y}\right)^{\mathrm{2}} ={x},\:\:\:{then}\:\int\frac{{dx}}{{x}−\mathrm{3}{y}}=? \\ $$ Answered by Frix last updated on 11/Sep/22 $${y}\left({x}−{y}\right)^{\mathrm{2}} ={x} \\ $$$${x}^{\mathrm{2}} {y}−\mathrm{2}{xy}^{\mathrm{2}}…