Question Number 116427 by bemath last updated on 04/Oct/20 $$\:\int\:\left(\mathrm{sec}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$ Answered by john santu last updated on 04/Oct/20 $$\:\int\:\left(\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right)^{\mathrm{2}} {dx}\:=\:\int\:\frac{\mathrm{1}−\mathrm{2sin}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}…
Question Number 116418 by bemath last updated on 03/Oct/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{5}} \:\sqrt{\mathrm{4}+\mathrm{x}^{\mathrm{2}} }}\:=? \\ $$ Answered by MJS_new last updated on 03/Oct/20 $$\int\frac{{dx}}{{x}^{\mathrm{5}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}= \\…
Question Number 116391 by bobhans last updated on 03/Oct/20 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}}\:}\:? \\ $$ Commented by TANMAY PANACEA last updated on 03/Oct/20 $${how}\:{to}\:{post}\:{question}… \\ $$$${here}\:{i}\:{am}\:{sharing}\:{intregation}…{Tanmay} \\ $$$$\int\frac{{sin}\theta}{{cos}\mathrm{3}\theta}+\frac{{sin}\mathrm{3}\theta}{{cos}\mathrm{9}\theta}+\frac{{sin}\mathrm{9}\theta}{{cos}\mathrm{27}\theta}\:{d}\theta…
Question Number 116385 by bemath last updated on 03/Oct/20 $$\:\int\:\frac{\mathrm{xe}^{\mathrm{x}} }{\:\sqrt{\mathrm{1}+\mathrm{e}^{\mathrm{x}} }}\:\mathrm{dx}\: \\ $$ Answered by MJS_new last updated on 03/Oct/20 $$\int\frac{\mathrm{e}^{{x}} {x}}{\:\sqrt{\mathrm{e}^{{x}} +\mathrm{1}}}{dx}= \\…
Question Number 116375 by mnjuly1970 last updated on 03/Oct/20 $$\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:{ordinary}\:{differential} \\ $$$${equation}\left({o}.{d}.{e}\right) \\ $$$$\:\:\: \\ $$$$\:\:\:{y}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:−\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} ={y}^{\mathrm{2}} \left({lny}\right)\:\:… \\ $$$$\:\:\:{find}\::\:\:{general}\:\:{solution} \\…
Question Number 50811 by ajfour last updated on 20/Dec/18 Commented by ajfour last updated on 20/Dec/18 $${Find}\:{distance}\:{between}\:{centres} \\ $$$${of}\:{the}\:{two}\:{equal}\:{ellipses}. \\ $$ Commented by ajfour last…
Question Number 181872 by srikanth2684 last updated on 01/Dec/22 $$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\frac{\mathrm{1}}{\mid{x}\mid}\:{dx} \\ $$ Answered by Frix last updated on 01/Dec/22 $$\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\frac{{dx}}{\mid{x}\mid}=\underset{\mathrm{0}} {\overset{\mathrm{1}}…
Question Number 181857 by KINMATICS last updated on 01/Dec/22 Answered by hmr last updated on 01/Dec/22 $$\int_{\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{2}}} \:\frac{{rcos}\left(\theta\right)}{{r}^{\mathrm{2}} }\:\:{r}\:{dr}\:{d}\theta \\ $$$$=\:\int_{\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{2}}}…
Question Number 116318 by Bird last updated on 03/Oct/20 $$\left.\mathrm{1}\right)\:{explicite}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({a}+{x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$$$\left.\mathrm{1}\left.\right)\:\mathrm{1}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{1}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$$${and}\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left(\mathrm{3}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$…
Question Number 116311 by bemath last updated on 03/Oct/20 $$\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{3}}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{2x}}{\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }\:\mathrm{dx}\: \\ $$$$ \\ $$ Answered by bobhans last updated on 03/Oct/20 $$\mathrm{let}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{u}\:\mathrm{with}\:\begin{cases}{\mathrm{u}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\\{\mathrm{u}=\mathrm{0}}\end{cases}…