Question Number 84766 by jagoll last updated on 15/Mar/20 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{16}+\mathrm{9sin}\:\mathrm{x}\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by jagoll last updated on 16/Mar/20 $$\int\:\mathrm{sec}\:\:\mathrm{x}\:\left[\:\frac{\mathrm{cos}\:\:\mathrm{x}}{\left(\mathrm{16}+\mathrm{9sin}\:\mathrm{x}\right)^{\mathrm{2}} }\right]\:\mathrm{dx}\:= \\…
Question Number 19230 by tawa tawa last updated on 07/Aug/17 Answered by ajfour last updated on 07/Aug/17 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{f}\left(\mathrm{x}\right)\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{f}\left(\mathrm{x}−\mathrm{2}\right)\sqrt[{\mathrm{3}}]{\mathrm{1}+…}}}}\: \\ $$$$\Rightarrow\:\left[\mathrm{g}\left(\mathrm{x}\right)\right]^{\mathrm{3}} =\mathrm{1}+\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}−\mathrm{1}\right) \\ $$$$\Rightarrow\:\mathrm{degree}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{1}. \\ $$$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{Ax}+\mathrm{B}…
Question Number 84759 by mathmax by abdo last updated on 15/Mar/20 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mind is power last updated…
Question Number 84733 by manr last updated on 15/Mar/20 $$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$ Answered by TANMAY PANACEA last updated on 15/Mar/20 $$ \\ $$$$\int\frac{\left({x}^{\mathrm{2}}…
Question Number 19195 by vivek last updated on 06/Aug/17 $$\int\frac{\mathrm{5}{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{5}} }{\left({x}^{\mathrm{5}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }\:\:\:{solve}\:{the}\:{intgration} \\ $$ Commented by vivek last updated on 07/Aug/17 $${please}\:{solve}\:{quetion} \\…
Question Number 84726 by M±th+et£s last updated on 15/Mar/20 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{.^{.^{.} } } } } {dy}=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$…
Question Number 84713 by john santu last updated on 15/Mar/20 $$\int\overset{\:\:\mathrm{1}} {\:}_{\mathrm{0}} \mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)\:\mathrm{dx}\:? \\ $$ Commented by TANMAY PANACEA last updated on 15/Mar/20…
Question Number 84708 by Power last updated on 15/Mar/20 Answered by TANMAY PANACEA last updated on 16/Mar/20 $$\int\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{5}}} \\ $$$$\int\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{2}} \sqrt{\left({x}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{6}}} \\…
Question Number 84702 by Power last updated on 15/Mar/20 Commented by abdomathmax last updated on 15/Mar/20 $${I}\:=\int\:\:\:\frac{{dx}}{{shx}+\mathrm{1}}\:\Rightarrow{I}=\int\:\:\frac{{dx}}{\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{2}}+\mathrm{1}}\:=\int\frac{\mathrm{2}{dx}}{{e}^{{x}} −{e}^{−{x}} \:+\mathrm{2}} \\ $$$$=_{{e}^{{x}} ={t}} \:\:\:\:\:\int\:\:\frac{\mathrm{2}}{{t}−{t}^{−\mathrm{1}}…
Question Number 84709 by M±th+et£s last updated on 15/Mar/20 $$\int\sqrt[{\mathrm{3}}]{{tan}\left({x}\right)}\:{dx} \\ $$ Answered by MJS last updated on 15/Mar/20 $$\int\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}}\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\left(\mathrm{tan}\:{x}\right)^{\mathrm{2}/\mathrm{3}} \:\rightarrow\:{dx}=\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{sin}\:{x}\right)^{\mathrm{1}/\mathrm{3}} \left(\mathrm{cos}\:{x}\right)^{\mathrm{5}/\mathrm{3}} {dt}\right]…