Question Number 118188 by mnjuly1970 last updated on 16/Oct/20 Commented by MJS_new last updated on 16/Oct/20 $${f}\left({x}\right)=\mathrm{e}^{−\frac{\mathrm{4}}{{x}^{\mathrm{2}} }} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\mathrm{0} \\ $$$$\underset{{x}\rightarrow\pm\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:=\mathrm{1} \\…
Question Number 52649 by Tawa1 last updated on 10/Jan/19 $$\int\:\frac{\mathrm{4x}^{\mathrm{2}} \:+\:\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Commented by maxmathsup by imad last updated on 10/Jan/19 $${et}\:{I}\:=\int\:\:\frac{\mathrm{4}{x}^{\mathrm{2}}…
Question Number 183709 by Michaelfaraday last updated on 30/Dec/22 Commented by Michaelfaraday last updated on 29/Dec/22 $${please}\:{who}\:{can}\:{help}\:{me}\:{on}\:{this} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 183706 by cortano1 last updated on 29/Dec/22 $$\:\:\:\:{A}=\int\:\frac{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{4}} {x}}\:{dx} \\ $$ Answered by Ar Brandon last updated on 29/Dec/22 $${A}=\int\frac{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{4}} {x}}{dx}=\int\frac{\mathrm{sec}^{\mathrm{4}}…
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Question Number 118145 by bemath last updated on 15/Oct/20 $$\int\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:? \\ $$ Commented by bobhans last updated on 15/Oct/20 $$\mathrm{Decomposition}\:\mathrm{fractional} \\ $$$$\:\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}}…
Question Number 118113 by bemath last updated on 15/Oct/20 $$\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }}\:=?\: \\ $$ Answered by Lordose last updated on 15/Oct/20 $$ \\ $$$$\mathrm{x}=\mathrm{asecu}\:\mathrm{dx}=\:\mathrm{secutanudu}…
Question Number 118111 by bemath last updated on 15/Oct/20 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by Lordose last updated on 15/Oct/20 $$ \\…
Question Number 118094 by bemath last updated on 15/Oct/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}+\mathrm{2}}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 15/Oct/20 $$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{cosxdx}}{\mathrm{2}{cosx}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{cosx}+\mathrm{1}}{dx} \\ $$$$=\frac{{x}}{\mathrm{2}}−\int\frac{\mathrm{1}}{\frac{\mathrm{2}−\mathrm{2}{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{1}}.\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 52550 by Tawa1 last updated on 09/Jan/19 $$\:\:\int_{\mathrm{0}} ^{\:\infty} \:\:\:\frac{\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{1}}\:\:\mathrm{dx}\: \\ $$ Commented by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}}…