Question Number 126661 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}… \\ $$$$\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{\mathrm{1}+{x}^{\mathrm{4}} {ln}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{6}} }\right){dx}=? \\ $$$$ \\ $$ Commented by Dwaipayan…
Question Number 126604 by bramlexs22 last updated on 22/Dec/20 $$\:\int\:\frac{{dx}}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\:\sqrt[{\mathrm{4}}]{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}}}\:? \\ $$ Answered by liberty last updated on 22/Dec/20 $${Y}=\int\:\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:\sqrt[{\mathrm{4}}]{\mathrm{2}{x}^{\mathrm{2}}…
Question Number 126601 by Lordose last updated on 22/Dec/20 $$\int_{\frac{\mathrm{1}}{\mathrm{n}}} ^{\:\frac{\mathrm{3}}{\mathrm{n}}} \mathrm{log}\left(\Gamma\left(\mathrm{x}\right)\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61056 by Tawa1 last updated on 28/May/19 $$\int\:\frac{\mathrm{x}\:+\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by perlman last updated on 28/May/19 $${cos}\left({x}\right)=\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)−\mathrm{1} \\ $$$$\frac{{x}+{sin}\left({x}\right)}{\mathrm{1}+{cos}\left({x}\right)}=\frac{{x}+{sin}\left({x}\right)}{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}=\frac{{x}}{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}+\frac{\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}\right){cos}\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{2}{cos}^{\mathrm{2}}…
Question Number 126586 by benjo_mathlover last updated on 22/Dec/20 $$\:\:\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}\:{dx}\:? \\ $$ Answered by liberty last updated on 22/Dec/20 $${partial}\:{fraction} \\ $$$$\:\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}\:=\:{P}\left(\frac{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}\right)+{Q}\:\frac{\frac{{d}}{{dx}}\left(\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\right)}{\mathrm{cos}\:{x}−\mathrm{sin}\:{x}} \\ $$$$\Leftrightarrow\:\mathrm{sin}\:{x}\:=\:{P}\left(\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\right)+{Q}\left(−\mathrm{sin}\:{x}−\mathrm{cos}\:{x}\right) \\…
Question Number 61045 by mathsolverby Abdo last updated on 28/May/19 $${calculate}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left(\mathrm{2}{arctanx}\right){dx} \\ $$$${and}\:{J}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left(\mathrm{2}{arctanx}\right){dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 126577 by benjo_mathlover last updated on 22/Dec/20 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\sqrt[{\mathrm{3}}]{\left(\mathrm{3}−{x}\right){x}^{\mathrm{2}} }\:{dx}\:=?\: \\ $$ Answered by Dwaipayan Shikari last updated on 22/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 61041 by mathsolverby Abdo last updated on 28/May/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left[\mathrm{2}{x}\right]−\left[{x}\right]}{{x}^{\mathrm{4}} }\:{dx}\: \\ $$ Commented by maxmathsup by imad last updated on 29/May/19…
Question Number 61039 by mathsolverby Abdo last updated on 28/May/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\frac{\mathrm{2}}{\mathrm{1}+{x}}\right){dx} \\ $$ Commented by maxmathsup by imad last updated on 29/May/19 $${let}\:{A}\:=\int_{\mathrm{0}}…
Question Number 126571 by benjo_mathlover last updated on 22/Dec/20 $$\:\:\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}\:^{\mathrm{2}} {x}−\mathrm{1}}}\:{dx}\:?\: \\ $$ Answered by MJS_new last updated on 22/Dec/20 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}^{\mathrm{2}} \:{x}\:−\mathrm{1}}}{dx}=\int\sqrt{\frac{\mathrm{tan}\:{x}}{\mathrm{tan}^{\mathrm{2}} \:{x}\:−\mathrm{1}}}{dx}= \\ $$$$=−\frac{\mathrm{i}}{\:\sqrt{\mathrm{2}}}\int\sqrt{\mathrm{tan}\:\mathrm{2}{x}}{dx}…