Question Number 93481 by mashallah last updated on 13/May/20 $$\int\left(\mathrm{log}\:\mathrm{x}/\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}= \\ $$ Commented by abdomathmax last updated on 15/May/20 $${I}\:=\int\:\frac{{lnx}}{{x}^{\mathrm{2}} }{dx}\:\:{by}\:{parts} \\ $$$${I}\:=−\frac{{lnx}}{{x}}\:−\int\:\left(−\frac{\mathrm{1}}{{x}}\right)×\frac{{dx}}{{x}}\:=−\frac{{lnx}}{{x}}\:+\int\:\frac{{dx}}{{x}^{\mathrm{2}} }…
Question Number 159008 by amin96 last updated on 11/Nov/21 $$\int\frac{\mathrm{6}^{{x}} }{\mathrm{4}^{{x}} +\mathrm{9}^{{x}} }{dx}=? \\ $$ Answered by qaz last updated on 11/Nov/21 $$\int\frac{\mathrm{6}^{\mathrm{x}} }{\mathrm{4}^{\mathrm{x}} +\mathrm{9}^{\mathrm{x}}…
Question Number 93473 by mashallah last updated on 13/May/20 $$\int\mathrm{1}/\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$ Commented by abdomathmax last updated on 15/May/20 $${A}\:=\int\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:{we}\:{do}\:{the}\:{changement}\:{x}\:={tant}\:\Rightarrow \\ $$$${A}\:\:=\int\:\:\:\frac{\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 93471 by mashallah last updated on 13/May/20 $$\int\mathrm{1}/\mathrm{1}+\mathrm{x2} \\ $$ Answered by Rio Michael last updated on 13/May/20 $$\int\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\:{dx}\:=\:\mathrm{arctan}\:{x}\:+\:{C} \\ $$ Terms…
Question Number 93467 by i jagooll last updated on 13/May/20 $$\int\:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{x}\right)^{\mathrm{3}} \:\mathrm{dx}\: \\ $$ Answered by john santu last updated on 13/May/20 Terms of Service…
Question Number 158993 by amin96 last updated on 11/Nov/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{xye}}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}^{\mathrm{2}} } \boldsymbol{\mathrm{dxdy}}=? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 158990 by cortano last updated on 11/Nov/21 $$\:\int\:\frac{\mathrm{sec}\:{x}}{\mathrm{sin}\:{x}+\mathrm{csc}\:{x}−\mathrm{1}}\:{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158973 by mnjuly1970 last updated on 11/Nov/21 Answered by qaz last updated on 11/Nov/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{x}}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }−\int_{\mathrm{0}}…
Question Number 158965 by cortano last updated on 11/Nov/21 $$\:\int\:\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{{x}}\:+\mathrm{1}}\:{dx}\:=? \\ $$ Answered by puissant last updated on 11/Nov/21 $$\Omega=\int\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{{x}}+\mathrm{1}}{dx} \\ $$$${u}=\sqrt{{x}}\:\rightarrow\:{du}=\frac{{dx}}{\mathrm{2}\sqrt{{x}}}\:\rightarrow\:{dx}=\mathrm{2}{udu} \\ $$$$\Rightarrow\:\Omega\:=\:\int\frac{\mathrm{2}{u}\sqrt{{u}^{\mathrm{2}} +\mathrm{1}}}{{u}+\mathrm{1}}{du}\:;\:…
Question Number 93410 by M±th+et+s last updated on 12/May/20 $$\int\frac{\mathrm{1}+{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{8}} }{dx} \\ $$ Commented by prakash jain last updated on 13/May/20 $$\mathrm{Were}\:\mathrm{you}\:\mathrm{able}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}.\:\mathrm{My}\: \\ $$$$\mathrm{method}\:\mathrm{of}\:\mathrm{solving}\:\mathrm{by}\:\mathrm{partial}…