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Category: Integration

some-practice-for-the-brave-cos-2-x-sin-2-x-cos-x-sin-x-dx-cos-2-x-tan-2-x-cos-x-tan-x-dx-sin-2-x-tan-2-x-sin-x-tan-x-dx-

Question Number 45802 by MJS last updated on 17/Oct/18 $$\mathrm{some}\:\mathrm{practice}\:\mathrm{for}\:\mathrm{the}\:\mathrm{brave}… \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{sin}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$ Commented…

find-dx-cosx-sin-2-x-

Question Number 45795 by maxmathsup by imad last updated on 16/Oct/18 $${find}\:\int\:\frac{{dx}}{{cosx}\:{sin}^{\mathrm{2}} {x}} \\ $$ Answered by MJS last updated on 17/Oct/18 $$\frac{\mathrm{1}}{\mathrm{cos}\:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}}=\left(\mathrm{1}+\frac{\mathrm{cos}^{\mathrm{2}} \:{x}}{\mathrm{sin}^{\mathrm{2}}…

find-f-x-0-cos-x-t-2-dtand-g-x-0-sin-x-t-2-dt-2-find-the-value-of-f-x-and-g-x-

Question Number 45771 by maxmathsup by imad last updated on 16/Oct/18 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}+{t}^{\mathrm{2}} \right){dtand}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}+{t}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{f}^{'} \left({x}\right)\:{and}\:{g}^{'} \left({x}\right). \\ $$ Answered…

Question-45706

Question Number 45706 by Meritguide1234 last updated on 15/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Oct/18 $${trying}\:{to}\:{solve}… \\ $$$$\int\frac{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)}{\left(\mathrm{1}−{x}^{\mathrm{4}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }\:}{dx} \\ $$$$\int\frac{\mathrm{1}+{x}^{\mathrm{4}} }{{x}^{\mathrm{2}}…

Question-45705

Question Number 45705 by Sanjarbek last updated on 15/Oct/18 Commented by maxmathsup by imad last updated on 16/Oct/18 $$\int\:{sin}\left({x}^{\mathrm{2}} \right){dx}\:=\frac{\sqrt{\pi}\left(\sqrt{\mathrm{2}}+{i}\sqrt{\mathrm{2}}\right){erf}\left\{\:\left(\sqrt{\mathrm{2}}+{i}\sqrt{\mathrm{2}}\right)\frac{{x}}{\mathrm{2}}\right\}+\sqrt{\pi}\left(\sqrt{\mathrm{2}}−{i}\sqrt{\mathrm{2}}\right){erf}\left\{\left(\sqrt{\mathrm{2}−}{i}\sqrt{\mathrm{2}}\right)\frac{{x}}{\mathrm{2}}\right\}}{\mathrm{8}} \\ $$$${this}\:{formulae}\:{is}\:{given}\:{by}\:{integral}\:{calculator}\:{so}\:{give}\:{me}\:{time}\:{to}\:{prof}\:{this}… \\ $$ Commented…

cos-1-sinx-dx-

Question Number 45670 by arvinddayama01@gmail.com last updated on 15/Oct/18 $$\int{cos}^{−\mathrm{1}} \left({sinx}\right){dx}=? \\ $$ Commented by maxmathsup by imad last updated on 15/Oct/18 $${let}\:{I}\:=\int\:{arccos}\left({sinx}\right){dx}\:\:{changement}\:{arcos}\left({sinx}\right)={t}\:\Rightarrow{sinx}={cost} \\ $$$$\Rightarrow{x}={arcsin}\left({cost}\right)\:\Rightarrow{dx}=−{sint}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{cos}^{\mathrm{2}}…