Question Number 71695 by peter frank last updated on 18/Oct/19 Answered by MJS last updated on 19/Oct/19 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\sqrt{\mathrm{tan}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{\mathrm{tan}\:{x}}\mathrm{cos}^{\mathrm{2}} \:{x}\:{dt}=\frac{\mathrm{2}{t}}{{t}^{\mathrm{4}} +\mathrm{1}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{4}}…
Question Number 137206 by JulioCesar last updated on 31/Mar/21 Answered by bemath last updated on 31/Mar/21 $$\mathrm{by}\:\mathrm{parts}\:\begin{cases}{\mathrm{u}=\mathrm{ln}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right) \:\mathrm{du}=\frac{\mathrm{2}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)}\mathrm{dx}}\\{\mathrm{v}\:=\:\mathrm{x}}\end{cases} \\ $$$$\mathrm{I}\:=\:\mathrm{x}\:\mathrm{ln}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right)−\int\:\frac{\mathrm{2x}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)}\mathrm{dx} \\ $$$$\mathrm{I}=\mathrm{x}\:\mathrm{ln}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right)−\left[\int\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\mathrm{dx}+\int\:\frac{\mathrm{1}}{\mathrm{x}+\mathrm{1}}\mathrm{dx}\:\right] \\ $$$$\mathrm{I}=\:\mathrm{x}\:\mathrm{ln}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right)−\mathrm{ln}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\:+\:\mathrm{C}…
Question Number 6087 by sanusihammed last updated on 12/Jun/16 $${Given}\:{the}\:{terms}\:\:\:\:{a}_{{k}} \:\:\:{and}\:\:{a}_{{k}\:+\:{r}\:} \:\:{of}\:{an}\:{A}.{P} \\ $$$${find}\:\:{a}_{\mathrm{1}} \:\:{and}\:\:{a}_{{k}\:+\:{r}} \:\:{in}\:{terms}\:{of}\:\:{a}_{{k}\:} \:{and}\:\:{a}_{{k}\:+\:{r}} \\ $$ Commented by Rasheed Soomro last updated…
Question Number 137065 by mr W last updated on 29/Mar/21 Commented by mr W last updated on 29/Mar/21 $${which}\:{number}\:{is}\:{larger}? \\ $$ Answered by mr W…
Question Number 137026 by metamorfose last updated on 29/Mar/21 $$\:\mathrm{2971}{x}\equiv\mathrm{1792}\left({mod}\:\mathrm{1000}\right)…{x}\in{Z}? \\ $$ Commented by yutytfjh67ihd last updated on 30/Mar/21 Commented by mr W last updated…
Question Number 137005 by greg_ed last updated on 28/Mar/21 $$\boldsymbol{\mathrm{Hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×…×\frac{\mathrm{223}}{\mathrm{224}}\:\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{S}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{4}}{\mathrm{5}}×\frac{\mathrm{6}}{\mathrm{7}}×…×\frac{\mathrm{224}}{\mathrm{225}}\:. \\ $$$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\::\:\:\boldsymbol{\mathrm{R}}\:<\:\frac{\mathrm{1}}{\mathrm{15}}\:<\:\boldsymbol{\mathrm{S}}. \\ $$ Commented by greg_ed last updated on 01/May/21…
Question Number 136987 by Ousmane last updated on 28/Mar/21 $$\Rightarrow\mathrm{2}{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5851 by sanusihammed last updated on 01/Jun/16 $${Solve}\:{simultaneously} \\ $$$$ \\ $$$$\mathrm{2}{x}\:+\:{y}\:−\:{z}\:=\:\mathrm{8}\:\:\:\:………\:\left({i}\right) \\ $$$${x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:………\:\left({ii}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{3}} \:+\:\mathrm{4}{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:………..\:\left({iii}\right) \\…
Question Number 5834 by sanusihammed last updated on 31/May/16 $${Find}\:{all}\:{positive}\:{integers}\:{n}\:{for}\:{which}\:{there}\:{exist} \\ $$$${non}−{negative}\:{integer}\:.\:{a}_{\mathrm{1}\:} {a}_{\mathrm{2}} \:{a}_{\mathrm{3}} \:…….\:{a}_{{n}} \:.\:{Such}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{3}} } }\:+\:….\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} }…
Question Number 71327 by TawaTawa last updated on 13/Oct/19 Answered by mind is power last updated on 13/Oct/19 $$\mathrm{ferma}\:\mathrm{lemma}\: \\ $$$$\mathrm{x}^{\mathrm{5}} =\mathrm{x}\left(\mathrm{5}\right) \\ $$$$\mathrm{x}^{\mathrm{4}} =\mathrm{1}\left(\mathrm{5}\right)\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:\mathrm{x}\neq\mathrm{0}…