Question Number 154192 by mnjuly1970 last updated on 15/Sep/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}.{sin}\left({ln}\left({x}\right)\right)}{\mathrm{1}−{x}}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:{method}\:\mathrm{1} \\ $$$$\:\:\:\:\:\Omega=\:\mathrm{I}{m}\left[\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:{x}^{\:{i}+\mathrm{1}} }{\mathrm{1}−{x}}\:{dx}=\Phi\right] \\ $$$$\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}}…
Question Number 154195 by rexford last updated on 15/Sep/21 $$\int\frac{{x}+{sinx}}{\mathrm{1}+{cosx}}{dx}\:\:\:\: \\ $$$${please},{help}\:{me} \\ $$ Answered by qaz last updated on 15/Sep/21 $$\because\:\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right)'=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}} \\ $$$$\therefore\int\frac{\mathrm{x}+\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\mathrm{dx} \\…
Question Number 154186 by daus last updated on 15/Sep/21 Answered by puissant last updated on 15/Sep/21 $$\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} \\ $$$$=\int{x}−\frac{\mathrm{4}{x}−\mathrm{3}}{{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}}{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} −\int\frac{\mathrm{4}{x}−\mathrm{3}}{{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}}{dx}…
Question Number 23108 by Kathie last updated on 26/Oct/17 $$\int\mathrm{e}^{−\mathrm{x}} \mathrm{sin2x}\:\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 26/Oct/17 $${I}=\int{e}^{−{x}} {sin}\mathrm{2}{xdx} \\ $$$${u}={sin}\mathrm{2}{x}\Rightarrow{u}'=\mathrm{2}{cos}\mathrm{2}{x} \\…
Question Number 154175 by daus last updated on 15/Sep/21 Commented by daus last updated on 15/Sep/21 integrate it Answered by EDWIN88 last updated on 15/Sep/21 $$\int\:\frac{\mathrm{32}{x}}{\left(\mathrm{2}{x}−\mathrm{1}\right)\left(\mathrm{2}{x}\:−\mathrm{3}\:\:\right)\left(\mathrm{2}{x}−\mathrm{5}\right)}\:{dx}…
Question Number 88616 by TawaTawa1 last updated on 11/Apr/20 Commented by jagoll last updated on 28/Apr/20 $$\mathrm{1}.{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{0}\:=\:\mathrm{0} \\ $$$${a}\:=\:\mathrm{1}\:,\:{b}\:=\:−\mathrm{4}\:,\:{c}\:=\:\mathrm{0} \\ $$ Commented by ajfour…
Question Number 88606 by TawaTawa1 last updated on 11/Apr/20 Commented by jagoll last updated on 12/Apr/20 $$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{line}\: \\ $$$$\mathrm{y}\:=\:\mathrm{mx}\:\Rightarrow\mathrm{4t}−\mathrm{t}^{\mathrm{2}} \:=\:\mathrm{m}.\mathrm{t}\: \\ $$$$\mathrm{m}\:=\:\mathrm{4}−\mathrm{t}\:\Rightarrow\mathrm{y}\:=\:\left(\mathrm{4}−\mathrm{t}\right)\mathrm{x} \\ $$$$\mathrm{line}\:\mathrm{and}\:\mathrm{parabolic}\:\mathrm{intersect} \\…
Question Number 154143 by mnjuly1970 last updated on 14/Sep/21 Answered by phanphuoc last updated on 14/Sep/21 $${u}=−{lnx}\rightarrow{e}^{−{u}} ={x}\rightarrow−{e}^{−{u}} {du}={dx} \\ $$$$\Omega=\int_{\infty} ^{\mathrm{0}} \frac{{e}^{−{x}} {sinx}}{\mathrm{1}+{e}^{−\mathrm{2}{x}} }\left(−{e}^{−{x}}…
Question Number 88603 by hovero clinton last updated on 11/Apr/20 Answered by TANMAY PANACEA. last updated on 11/Apr/20 $${x}={sina} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{lnsina}×{cosada}}{\left(\mathrm{1}+\mathrm{8}{sin}^{\mathrm{2}} {a}\right){cosa}} \\…
Question Number 154142 by EDWIN88 last updated on 14/Sep/21 Answered by mr W last updated on 14/Sep/21 $${y}={a}\left({x}−\mathrm{4}\right)\left({x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\mathrm{8}={a}\left(−\mathrm{4}\right)\left(+\mathrm{2}\right)^{\mathrm{2}} \:\Rightarrow{a}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${y}=−\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{4}\right)\left({x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$\frac{{dy}}{{dx}}=−\frac{\mathrm{1}}{\mathrm{2}}\left[\left({x}+\mathrm{2}\right)^{\mathrm{2}}…