Question Number 156864 by mnjuly1970 last updated on 16/Oct/21 $$ \\ $$$$\:\:\:\:\phi\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\:\left(\mathrm{1}−{x}^{\:\mathrm{2}} \right)}{\mathrm{1}+\:{x}^{\:\mathrm{2}} }\:{dx}\:= \\ $$$$\:\:{proof}\:: \\ $$$$\:\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}−{x}\:\right)}{\mathrm{1}+{x}^{\:\mathrm{2}} }{dx}\:+\:\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:\:….\:\mathrm{I}=\:\int_{\mathrm{0}}…
Question Number 91329 by niroj last updated on 29/Apr/20 $$\:\mathrm{S}\boldsymbol{\mathrm{olve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}+\boldsymbol{\mathrm{xy}}\:=\:\boldsymbol{\mathrm{x}} \\ $$ Commented by MWSuSon last updated on 30/Apr/20 $${do}\:{you}\:{need}\:{a}\:{specific}\:{method}?…
Question Number 156824 by Tawa11 last updated on 15/Oct/21 $$\mathrm{If}\:\:\:\:\:\:\mathrm{x}\:\:\:−\:\:\:\mathrm{z}\:\:\:\:=\:\:\:\:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{yz}\right)\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{z}\:\:\:=\:\:\:\mathrm{z}\left(\mathrm{x},\:\:\mathrm{y}\right),\:\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{x}}\:,\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{y}} \\ $$ Answered by mr W last updated on 16/Oct/21 $$\mathrm{1}−\frac{\partial{z}}{\partial{x}}=\frac{{y}}{\mathrm{1}+{y}^{\mathrm{2}} {z}^{\mathrm{2}} }×\frac{\partial{z}}{\partial{x}} \\…
Question Number 156776 by mnjuly1970 last updated on 15/Oct/21 $$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left({n}\:{ln}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}\right)\:−\mathrm{1}\right)=? \\ $$$$ \\ $$ Commented by CAIMAN last updated on 15/Oct/21…
Question Number 91185 by Tony Lin last updated on 28/Apr/20 $${f}\left({x}\right)=\left({x}−\mathrm{3}\right)^{\mathrm{5}} {ln}\left(\mathrm{1}+{x}\right) \\ $$$${f}^{\left(\mathrm{2020}\right)} \left(\mathrm{3}\right)=? \\ $$ Commented by Tony Lin last updated on 28/Apr/20…
Question Number 25572 by hoangnampham13 last updated on 11/Dec/17 $${Solve}\:{the}\:{differential}\:{equation}: \\ $$$${y}'\:=\:{cosh}\left({x}+{y}\right) \\ $$ Answered by prakash jain last updated on 11/Dec/17 $${y}'\:=\:{cosh}\left({x}+{y}\right)\:\:\:\left({A}\right) \\ $$$${u}\left({x}\right)={y}\left({x}\right)+{x}…
Question Number 156617 by mnjuly1970 last updated on 13/Oct/21 Answered by mindispower last updated on 14/Oct/21 $${e}^{−{x}} ={t} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{t}\right)\left(\mathrm{1}−{t}\right)}{\mathrm{1}+{t}}.\frac{{dt}}{{t}} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 25528 by Mahesh Andiboina last updated on 11/Dec/17 Commented by Mahesh Andiboina last updated on 11/Dec/17 $$\mathrm{plz}\:\mathrm{ans}\:\mathrm{both} \\ $$ Answered by sushmitak last…
Question Number 25520 by Mahesh Andiboina last updated on 11/Dec/17 Commented by Mahesh Andiboina last updated on 11/Dec/17 $$\mathrm{plzz}\:\mathrm{ans}\:\mathrm{both} \\ $$ Answered by prakash jain…
Question Number 25521 by Mahesh Andiboina last updated on 11/Dec/17 Answered by sushmitak last updated on 11/Dec/17 $$\mathrm{16} \\ $$$$\frac{{dy}}{{dx}}=\frac{{dy}/{dt}}{{dx}/{dt}}=\frac{\frac{{d}}{{dt}}\left(\mathrm{2}{at}\right)}{\frac{{d}}{{dt}}\left({at}^{\mathrm{2}} \right)}=\frac{\mathrm{2}{a}}{\mathrm{2}{at}}=\frac{\mathrm{1}}{{t}} \\ $$$$\mathrm{17} \\ $$$$\frac{{dy}}{{dx}}=\frac{{dy}/{dt}}{{dx}/{dt}}=\frac{\frac{{d}}{{dt}}\left({t}^{\mathrm{2}}…