Question Number 216381 by glory86 last updated on 06/Feb/25 $$\int\left({lnx}\right)^{\mathrm{2}} {dx} \\ $$ Answered by mr W last updated on 06/Feb/25 $$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} {dx} \\ $$$$={x}\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}}…
Question Number 216372 by glory86 last updated on 06/Feb/25 $$\int\frac{{xe}^{{x}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by MrGaster last updated on 06/Feb/25 $$\mathrm{Let}\:{u}={x}+\mathrm{1}\Rightarrow{du}={dx},{x}={u}−\mathrm{1} \\ $$$$\int\frac{\left({u}−\mathrm{1}\right){e}^{{u}−\mathrm{1}} }{{u}^{\mathrm{2}}…
Question Number 216388 by Tawa11 last updated on 06/Feb/25 Commented by Tawa11 last updated on 06/Feb/25 $$\mathrm{Q111432} \\ $$ Answered by mr W last updated…
Question Number 216390 by jucimar last updated on 06/Feb/25 $${f}\left({x}\right)={ax}\: \\ $$ Commented by issac last updated on 07/Feb/25 $${f}\left({x}\right)={ax}….??\: \\ $$ Commented by MrGaster…
Question Number 216387 by Tawa11 last updated on 06/Feb/25 Answered by mr W last updated on 06/Feb/25 $$\left(\mathrm{6},\:\mathrm{0}\right)\: \\ $$$$\left(\mathrm{6}−\mathrm{6}\right)^{\mathrm{2}} +\left(\mathrm{0}−\mathrm{3}+{a}\right)^{\mathrm{2}} =\mathrm{5}^{\mathrm{2}} \\ $$$$\Rightarrow−\mathrm{3}+{a}=\mathrm{5}\:\Rightarrow{a}=\mathrm{8} \\…
Question Number 216350 by issac last updated on 05/Feb/25 $$\mathcal{S}\:\mathrm{is}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{surrounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{cylinder}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9} \\ $$$$\mathrm{and}\:\mathrm{plane}\:{z}=\mathrm{0}\:,\:{z}=\mathrm{2}\:\mathrm{and} \\ $$$$\mathrm{and}\:\mathrm{vector}\:\mathrm{Field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=\mathrm{3}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{yz}\overset{\rightarrow}…
Question Number 216367 by Ismoiljon_008 last updated on 05/Feb/25 Answered by Rasheed.Sindhi last updated on 06/Feb/25 $$\underset{{n}=\mathrm{1}} {\overset{\mathrm{2021}} {\sum}}\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$$${a}_{{n}} =\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 216351 by issac last updated on 05/Feb/25 $$\mathrm{Vector}\:\mathrm{field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R}^{\mathrm{3}} \\ $$$$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={xy}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −\mathrm{5}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −\mathrm{3}{yz}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\underset{\mathcal{S};{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}}…
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Question Number 216363 by Ismoiljon_008 last updated on 05/Feb/25 Commented by A5T last updated on 05/Feb/25 $$\mathrm{Q207018} \\ $$ Commented by Ismoiljon_008 last updated on…