Question Number 149156 by gsk2684 last updated on 03/Aug/21 $${if}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{2012}}]{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{1012}} \left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{3012}} }}=\frac{\alpha}{\mathrm{2}\beta}\left(\mathrm{1}−{f}\left({x}\right)\right)^{\frac{\beta}{\alpha}} \\ $$$${then}\:{find}\:\alpha,\beta,{f}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18066 by tawa tawa last updated on 14/Jul/17 $$\left(\mathrm{a}\right)\:\:\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}:\:\:\mathrm{y}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\mathrm{1}}{\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{3}} \\ $$$$\left(\mathrm{b}\right)\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\mathrm{in}\:\mathrm{the}\:\mathrm{identity}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} \:−\:\mathrm{ax}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)}\:\equiv\:\frac{\mathrm{A}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)}\:+\:\frac{\mathrm{Bx}\:+\:\mathrm{Ca}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)} \\ $$$$\mathrm{where}\:\:\mathrm{a}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant},\:\:\mathrm{hence}\:\mathrm{prove}\:\mathrm{that}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}}…
Question Number 83603 by jagoll last updated on 04/Mar/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{x}} \\ $$ Commented by turbo msup by abdo last updated on 04/Mar/20 $${we}\:{use}\:{the}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t} \\ $$$$\Rightarrow\int\:\:\frac{{dx}}{\mathrm{1}−\mathrm{2}{cosx}}\:=\int\:\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 83597 by dennis kenneth last updated on 04/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}\right){dx} \\ $$ Commented by Jidda28 last updated on 04/Mar/20 $$\left.=\:\:{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}}…
Question Number 149113 by bramlexs22 last updated on 03/Aug/21 $$\:\int_{\mathrm{0}} ^{\:\pi} \:\frac{\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{7}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 03/Aug/21…
Question Number 149112 by bramlexs22 last updated on 03/Aug/21 $$\:\varphi\:=\:\int\:\mathrm{tan}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{3}}\right)\mathrm{tan}\:\mathrm{3x}\:\mathrm{tan}\:\left(\mathrm{2x}−\frac{\pi}{\mathrm{3}}\right)\:\mathrm{dx}\:=? \\ $$ Commented by som(math1967) last updated on 03/Aug/21 $$\boldsymbol{{tan}}\mathrm{3}\boldsymbol{{x}}=\boldsymbol{{tan}}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\:+\mathrm{2}\boldsymbol{{x}}−\frac{\boldsymbol{\pi}}{\mathrm{3}}\right) \\ $$$$\boldsymbol{{tan}}\mathrm{3}\boldsymbol{{x}}=\frac{\boldsymbol{{tan}}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)+\boldsymbol{{tan}}\left(\mathrm{2}\boldsymbol{{x}}−\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)}{\mathrm{1}−{tan}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)\boldsymbol{{tan}}\left(\mathrm{2}\boldsymbol{{x}}+\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{3}}\right)} \\ $$$$\therefore\boldsymbol{{tan}}\mathrm{3}\boldsymbol{{xtan}}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)\boldsymbol{{tan}}\left(\mathrm{2}\boldsymbol{{x}}−\frac{\boldsymbol{\pi}}{\mathrm{3}}\right) \\…
Question Number 83569 by mathmax by abdo last updated on 03/Mar/20 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Commented by mathmax by abdo last updated…
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Question Number 18024 by mondodotto@gmail.com last updated on 13/Jul/17 Answered by sma3l2996 last updated on 14/Jul/17 $${I}=\int\frac{\mathrm{5}{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}{dx}=\frac{\mathrm{5}}{\mathrm{2}}\int\frac{\mathrm{2}{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}{dx}+\int\frac{\mathrm{3}{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}} \\ $$$$=\frac{\mathrm{5}}{\mathrm{2}}\int\frac{\mathrm{2}{x}+\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}+\int\frac{\mathrm{3}−\mathrm{10}}{\:\sqrt{\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\mathrm{6}}}{dx} \\…
Question Number 149080 by Integrals last updated on 02/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com