Question Number 37451 by ajfour last updated on 13/Jun/18 $$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta{d}\theta}{\:\sqrt{{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta+{b}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta}}\:=\:? \\ $$ Commented by MJS last updated…
Question Number 37449 by gunawan last updated on 13/Jun/18 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}= \\ $$ Answered by ajfour last updated on 13/Jun/18 $$\mathrm{3}{x}^{\mathrm{3}}…
Question Number 37432 by MJS last updated on 13/Jun/18 $$\int\frac{{d}\alpha}{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{tan}\:\alpha\:+\mathrm{2cot}\:\frac{\alpha}{\mathrm{2}}}=? \\ $$$$\int\frac{{d}\beta}{\mathrm{2tan}\:\frac{\beta}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cot}\:\beta}=? \\ $$ Answered by ajfour last updated on 13/Jun/18 $$\int\frac{\mathrm{2sin}\:\alpha\mathrm{cos}\:\alpha{d}\alpha}{\mathrm{sin}\:^{\mathrm{2}} \alpha+\mathrm{4cos}\:^{\mathrm{2}} \alpha}=\int\frac{\mathrm{sin}\:\mathrm{2}\alpha{d}\alpha}{\mathrm{1}+\frac{\mathrm{3}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}\alpha\right)} \\…
Question Number 37425 by MJS last updated on 13/Jun/18 $$\int\frac{{x}^{\mathrm{5}} −\mathrm{3}{x}^{\mathrm{4}} −\mathrm{23}{x}^{\mathrm{3}} +\mathrm{51}{x}^{\mathrm{2}} +\mathrm{94}{x}−\mathrm{120}}{\mathrm{8}{x}^{\mathrm{3}} \sqrt{\mathrm{42}+{x}−{x}^{\mathrm{2}} }}{dx}=? \\ $$ Answered by ajfour last updated on 13/Jun/18…
Question Number 168499 by infinityaction last updated on 12/Apr/22 Answered by MJS_new last updated on 12/Apr/22 $$\left(\mathrm{1}\right)\:{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:{u}=\frac{\sqrt{\mathrm{1}−{t}}}{\:\sqrt{\mathrm{1}+{t}}} \\ $$$$\Rightarrow \\ $$$$−\int\left({u}^{\mathrm{10}} +{u}^{\mathrm{6}} \right){du}…
Question Number 168477 by infinityaction last updated on 11/Apr/22 Commented by mr W last updated on 11/Apr/22 $$\pi/\mathrm{3}>\mathrm{1} \\ $$$$\Rightarrow\mathrm{cos}^{−\mathrm{1}} \left(\pi/\mathrm{3}\right)\:{is}\:{not}\:{defined}! \\ $$$${question}\:{is}\:{wrong}! \\ $$…
Question Number 168473 by Mastermind last updated on 11/Apr/22 $${Integrate}: \\ $$$$\int\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by MJS_new last updated on…
Question Number 37404 by ajfour last updated on 12/Jun/18 $$\int_{\mathrm{0}} ^{\:\:\mathrm{2}\pi} \sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{2}{ab}\mathrm{cos}\:\theta}\:{d}\theta\: \\ $$$$\:\:\:\:{with}\:\:{a}>{b}>\mathrm{0}\:. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Jun/18…
Question Number 102926 by mohammad17 last updated on 11/Jul/20 $$\:\int\:\frac{{d}\theta}{\mathrm{2}{sin}^{\mathrm{2}} \theta−{cos}^{\mathrm{2}} \theta}\:\:? \\ $$ Answered by OlafThorendsen last updated on 11/Jul/20 $$\int\frac{{d}\theta}{\mathrm{2}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }−\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}…
Question Number 102922 by mohammad17 last updated on 11/Jul/20 $$\int\:\frac{{dx}}{{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{5}}\:\:? \\ $$ Commented by prakash jain last updated on 11/Jul/20 $$\mathrm{The}\:\mathrm{approach}\:\mathrm{you}\:\mathrm{take}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\mathrm{the}\:\mathrm{question} \\…