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Question Number 120461 by Khalmohmmad last updated on 31/Oct/20 $$\int\mathrm{sin}\left(\mathrm{ln}{x}\right){dx} \\ $$ Answered by Dwaipayan Shikari last updated on 31/Oct/20 $$\int{sin}\left({logx}\right){dx} \\ $$$$=\left(\int{e}^{{t}} {sin}\left({t}\right){dt}\:\right)\rightarrow{I}\:\:\:\:\:\:\:\:{logx}={t} \\…

Question Number 54909 by Hassen_Timol last updated on 14/Feb/19 $${Do}\:{you}\:{know}\:{a}\:{geometrical}\:{proof} \\ $$$${of}\:{the}\:{irrationality}\:{of}\:{number}\:\sqrt{\mathrm{2}}\:? \\ $$ Commented by kaivan.ahmadi last updated on 14/Feb/19 https://jeremykun.com/2011/08/14/the-square-root-of-2-is-irrational-geometric-proof/ Commented by kaivan.ahmadi…

Question Number 120422 by help last updated on 31/Oct/20 Commented by help last updated on 31/Oct/20 $${Q}\mathrm{5}? \\ $$ Commented by TANMAY PANACEA last updated…

Question Number 54880 by Otchere Abdullai last updated on 14/Feb/19 $${If}\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} ={a}^{\mathrm{2}} \:\:{find}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:{if}\:{a}\:{is} \\ $$$${constant}. \\ $$ Answered by kaivan.ahmadi last updated…

Question Number 185951 by manxsol last updated on 30/Jan/23 $$\int{x}^{\mathrm{3}} {ln}\left({x}+\mathrm{4}\right){dx} \\ $$ Answered by SEKRET last updated on 30/Jan/23 $$\:\int\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \centerdot\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{4}\right)\:\boldsymbol{\mathrm{dx}}= \\ $$$$\:\:=\frac{\boldsymbol{\mathrm{x}}^{\mathrm{4}} }{\mathrm{4}}\centerdot\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}+\mathrm{4}\right)\:−\:\int\:\frac{\boldsymbol{\mathrm{x}}^{\mathrm{4}}…