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Question Number 44695 by manish00@gmail.com last updated on 03/Oct/18 $$\int\frac{\boldsymbol{\mathrm{e}}^{\sqrt{\boldsymbol{\mathrm{t}}−\mathrm{1}}} }{\boldsymbol{\mathrm{t}}}\boldsymbol{\mathrm{dt}}\:=\:? \\ $$ Commented by maxmathsup by imad last updated on 04/Oct/18 $${changement}\:\sqrt{{t}−\mathrm{1}}={x}\:{give}\:{t}−\mathrm{1}={x}^{\mathrm{2}} \:\Rightarrow \\…
Question Number 110218 by 150505R last updated on 27/Aug/20 Answered by 1549442205PVT last updated on 28/Aug/20 $$\mathrm{Let}\:\mathrm{ABCD}\:\mathrm{be}\:\mathrm{trapezum}\:\mathrm{with}\:\mathrm{AB}//\mathrm{CD} \\ $$$$\mathrm{Through}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{A}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{line}\:\mathrm{d} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{diagonal}\:\mathrm{BD}\:\mathrm{we}\:\mathrm{have} \\ $$$$\mathrm{ABDE}\left(\mathrm{E}=\mathrm{d}\cap\left[\mathrm{CD}\right)\right)\mathrm{is}\:\mathrm{a}\:\mathrm{paralelogram} \\ $$$$,\mathrm{so}\:\mathrm{AB}=\mathrm{DE}.\mathrm{From}\:\mathrm{the}\:\mathrm{hypothesis}\:\mathrm{we}…
Question Number 110215 by 150505R last updated on 27/Aug/20 Commented by 150505R last updated on 27/Aug/20 $${please}\:{solve}… \\ $$ Answered by mathmax by abdo last…
Question Number 44674 by MJS last updated on 03/Oct/18 $$\mathrm{solving}\:\mathrm{some}\:\mathrm{integrals}\:\mathrm{we}\:\mathrm{might}\:\mathrm{meet}\:\mathrm{some} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{functions}\:\mathrm{which}\:\mathrm{cannot}\:\mathrm{be} \\ $$$$\mathrm{solved}\:\mathrm{with}\:\mathrm{elementar}\:\mathrm{knowledge}\:\mathrm{but}\:\mathrm{tables} \\ $$$$\mathrm{should}\:\mathrm{exist}\:\mathrm{somewhere}\:\mathrm{in}\:\mathrm{the}\:\mathrm{depth}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{www}… \\ $$$$\mathrm{these}\:\mathrm{links}\:\mathrm{might}\:\mathrm{be}\:\mathrm{interesting} \\ $$$$ \\ $$$$\mathrm{exponential}\:\mathrm{integral} \\…
Question Number 110203 by Don08q last updated on 27/Aug/20 Answered by Dwaipayan Shikari last updated on 27/Aug/20 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)^{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}−{x}}+\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }+….=\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}}=\frac{{x}−\mathrm{1}}{{x}}=\mathrm{1}−\frac{\mathrm{1}}{{x}} \\ $$$$\int\mathrm{1}−\frac{\mathrm{1}}{{x}}{dx}={x}−{logx}+{C} \\…
Question Number 44654 by manish00@gmail.com last updated on 02/Oct/18 $$\int\frac{\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by maxmathsup by imad last updated on 02/Oct/18 $${changement}\:{x}={tan}\theta\:{give}\:{I}\:=\int\:\:\frac{{e}^{{tan}\theta} }{\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 44639 by arvinddayama01@gmail.com last updated on 02/Oct/18 $$\int\frac{\mathrm{1}}{\mathrm{1}+\left(\boldsymbol{\mathrm{log}}\:\boldsymbol{\mathrm{x}}\right)^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=? \\ $$$$ \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 $${t}={lnx}\:\:{x}={e}^{{t}\:\:} \:\:\:{dx}={e}^{{t}} \:\:{dt}…
Question Number 175697 by Tawa11 last updated on 05/Sep/22 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{3x}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:−\:\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{2}}}\:\mathrm{dx} \\ $$ Answered by MJS_new last updated on 05/Sep/22 $$\underset{\mathrm{0}}…
Question Number 110143 by I want to learn more last updated on 27/Aug/20 Answered by mathdave last updated on 27/Aug/20 $${solution}\:{to}\:{question}\:\mathrm{1} \\ $$$${let}\:\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\left(\mathrm{1}−{x}^{{n}}…