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Category: Integration

x-sin-x-dx-

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} \\…

1-1-ln-x-

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…

calculate-U-n-1-n-n-2-x-2-y-2-e-x-2-y-2-dxdy-and-lim-n-U-n-

Question Number 110451 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\left[\frac{\mathrm{1}}{\mathrm{n}},\mathrm{n}\left[^{\mathrm{2}} \right.\right.} \:\:\:\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} } \mathrm{dxdy} \\ $$$$\mathrm{and}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$…

prove-that-1-t-1-t-2-dt-ln-1-1-t-2-C-

Question Number 44781 by arvinddayama01@gmail.com last updated on 04/Oct/18 $$\boldsymbol{{prove}}\:\boldsymbol{{that}}:−\:\int\frac{\mathrm{1}}{\boldsymbol{\mathrm{t}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\:=\:\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\sqrt{\mathrm{1}−\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\right)+\boldsymbol{\mathrm{C}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Oct/18 $$\int\frac{{tdt}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}−{t}^{\mathrm{2}} }\:} \\…