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Author: Tinku Tara

0-ln-1-x-x-x-2-x-1-dx-

Question Number 154202 by mathdanisur last updated on 15/Sep/21 $$\boldsymbol{\Omega}\:\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\centerdot\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\mathrm{x}\centerdot\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$ Answered by qaz last updated on 15/Sep/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}}…

log-2-x-log-4-y-4-x-y-8-

Question Number 88663 by mary_ last updated on 12/Apr/20 $$\begin{cases}{{log}_{\mathrm{2}} {x}+{log}_{\mathrm{4}} {y}=\mathrm{4}}\\{{x}.{y}=\mathrm{8}}\end{cases} \\ $$ Answered by jagoll last updated on 28/Apr/20 $$\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mathrm{2}} \left(\frac{\mathrm{8}}{\mathrm{x}}\right)\:=\mathrm{4} \\…

0-1-x-sin-ln-x-1-x-dx-method-1-Im-0-1-x-i-1-1-x-dx-0-1-x-i-1-x-i-2-1-x-2-dx-x-2

Question Number 154192 by mnjuly1970 last updated on 15/Sep/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}.{sin}\left({ln}\left({x}\right)\right)}{\mathrm{1}−{x}}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:{method}\:\mathrm{1} \\ $$$$\:\:\:\:\:\Omega=\:\mathrm{I}{m}\left[\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:{x}^{\:{i}+\mathrm{1}} }{\mathrm{1}−{x}}\:{dx}=\Phi\right] \\ $$$$\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}}…

x-sinx-1-cosx-dx-please-help-me-

Question Number 154195 by rexford last updated on 15/Sep/21 $$\int\frac{{x}+{sinx}}{\mathrm{1}+{cosx}}{dx}\:\:\:\: \\ $$$${please},{help}\:{me} \\ $$ Answered by qaz last updated on 15/Sep/21 $$\because\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right)'=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}} \\ $$$$\therefore\int\frac{\mathrm{x}+\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\mathrm{dx} \\…

Question-154194

Question Number 154194 by chinomso last updated on 15/Sep/21 Commented by alisiao last updated on 15/Sep/21 $$\int_{\mathrm{9}} ^{\:\mathrm{11}} \:\frac{\boldsymbol{{y}}+\mathrm{8}}{\boldsymbol{{c}}}\:\boldsymbol{{dy}}\:=\:\mathrm{1}\:\Rightarrow\:\frac{\mathrm{1}}{\boldsymbol{{c}}}\:\int_{\mathrm{9}} ^{\:\mathrm{11}} \:\left(\boldsymbol{{y}}+\mathrm{8}\right)\boldsymbol{{dy}}\:=\mathrm{1} \\ $$$$ \\ $$$$\boldsymbol{{c}}\:=\:\left(\frac{\boldsymbol{{y}}^{\mathrm{2}}…

Question-154186

Question Number 154186 by daus last updated on 15/Sep/21 Answered by puissant last updated on 15/Sep/21 $$\Omega=\int\frac{{x}^{\mathrm{3}} −\mathrm{7}{x}^{\mathrm{2}} +\mathrm{8}{x}+\mathrm{3}}{{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}}{dx} \\ $$$$=\int{x}−\frac{\mathrm{4}{x}−\mathrm{3}}{{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}}{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} −\int\frac{\mathrm{4}{x}−\mathrm{3}}{{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}}{dx}…