Question Number 131529 by mnjuly1970 last updated on 05/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:\ast\ast\ast\ast\ast\ast\ast\ast\ast\ast\:\:\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}\::::\::: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}^{\mathrm{4}} \right){ln}\left({x}\right)}{{x}}{dx}=−\frac{\boldsymbol{\pi\gamma}}{\mathrm{32}} \\ $$$$\:\:\:\:{note}\::\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\right){ln}\left({x}\right)}{{x}}{dx}\overset{{why}???} {=}\:\frac{−\boldsymbol{\pi\gamma}}{\mathrm{2}} \\ $$$$\:\:\:\:\boldsymbol{\phi}\overset{\langle{x}^{\mathrm{4}} ={t}\rangle}…
Question Number 459 by Karting7442 last updated on 25/Jan/15 $$\underset{} {{f}actor}\:{the}\:{expression}\:{completely}:\:\frac{\mathrm{3}}{\mathrm{4}}{a}−\frac{\mathrm{9}}{\mathrm{20}} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\frac{\mathrm{3}}{\mathrm{4}}{a}−\frac{\mathrm{9}}{\mathrm{20}}=\frac{\mathrm{3}}{\mathrm{4}}\left({a}−\frac{\mathrm{3}}{\mathrm{5}}\right) \\ $$ Terms…
Question Number 65992 by naka3546 last updated on 07/Aug/19 $${x}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{1}!}\:+\:\frac{\mathrm{1}}{\mathrm{4}\centerdot\mathrm{2}!}\:+\:\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{3}!}\:+\:\ldots\:+\:\frac{\mathrm{1}}{\mathrm{1002}\centerdot\mathrm{1000}!} \\ $$$${x}\centerdot\mathrm{1000}!\:\:=\:\:? \\ $$ Commented by Prithwish sen last updated on 08/Aug/19 $$\mathrm{last}\:\mathrm{term}\:\frac{\mathrm{n}}{\left(\mathrm{n}+\mathrm{1}\right)!}\:\:\mathrm{where}\:\mathrm{n}=\:\mathrm{1001} \\ $$$$\therefore\:\left[\frac{\mathrm{n}+\mathrm{1}−\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}\right]\:=\:\frac{\mathrm{1}}{\mathrm{n}!}\:−\:\frac{\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}…
Question Number 457 by lun last updated on 25/Jan/15 $$\mathrm{5}{x}+\mathrm{1}=\mathrm{0} \\ $$ Answered by lun last updated on 09/Jan/15 $$\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$ Commented by prakash…
Question Number 456 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}:\:\:\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{6}=\mathrm{11} \\ $$$$ \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{6}=\mathrm{11} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{x}=\mathrm{11}−\mathrm{6}…
Question Number 131525 by mathlove last updated on 05/Feb/21 $$\:{if}\:\:\:\left({a}−{b}\right)\left({a}+{b}\right)=\mathrm{23} \\ $$$${then}\:\:{faind}\:\:\:{a}\centerdot{b}=? \\ $$ Answered by mr W last updated on 05/Feb/21 $${no}\:{unique}\:{solution}\:{for}\:{a},{b}\in{R}. \\ $$$${for}\:{a},{b}\in{Z}:…
Question Number 131527 by Sudip last updated on 05/Feb/21 Answered by Dwaipayan Shikari last updated on 05/Feb/21 $$\frac{\mathrm{2}}{\mathrm{7}}\int\frac{{t}}{{t}+\frac{\mathrm{22}}{\mathrm{7}}}{dt}+\frac{\mathrm{5}}{\mathrm{7}}\int\frac{\mathrm{1}}{{t}+\frac{\mathrm{22}}{\mathrm{7}}}{dt} \\ $$$$=\frac{\mathrm{2}}{\mathrm{7}}{t}−\frac{\mathrm{44}}{\mathrm{49}}{log}\left({t}+\frac{\mathrm{22}}{\mathrm{7}}\right)+\frac{\mathrm{5}}{\mathrm{7}}{log}\left({t}+\frac{\mathrm{22}}{\mathrm{7}}\right) \\ $$ Answered by mr…
Question Number 65988 by mmkkmm000m last updated on 07/Aug/19 $$\int{dx}/{x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on 07/Aug/19 $${let}\:{A}\:=\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:\Rightarrow{A}\:=\int\:\:\:\frac{{dx}}{\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:+\frac{\mathrm{3}}{\mathrm{4}}}…
Question Number 453 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}\:\:\:\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$$$\mathrm{42}{x}−\mathrm{45}=−\mathrm{72} \\ $$$$\mathrm{42}{x}=−\mathrm{72}+\mathrm{45}…
Question Number 451 by Karting7442 last updated on 25/Jan/15 $${solve}\:{the}\:{equation}\:{for}\:{x}\:\::\:\mathrm{5}−{x}=\:−\mathrm{3} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{5}−{x}=−\mathrm{3} \\ $$$${x}=\mathrm{5}+\mathrm{3}=\mathrm{8} \\ $$…