Question Number 116554 by Bird last updated on 04/Oct/20 $${study}\:{the}\:{integral}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}^{{n}} {x}}{{x}^{{n}} }{dx} \\ $$$${n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$ Answered by Olaf last updated on 05/Oct/20…
Question Number 116533 by Bird last updated on 04/Oct/20 $${find}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}^{{n}} {x}}{{x}}{dx}\:\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$ Answered by Olaf last updated on 04/Oct/20 $$\mathrm{1st}\:\mathrm{case}\::\:{n}\:\mathrm{is}\:\mathrm{odd} \\…
Question Number 116500 by bobhans last updated on 04/Oct/20 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by Olaf last updated on 04/Oct/20 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{3}}…
Question Number 116501 by bemath last updated on 04/Oct/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx}\:? \\ $$ Answered by TANMAY PANACEA last updated on 04/Oct/20 $$\frac{{d}}{{dx}}\left({sinx}+{cosx}\right)={cosx}−{sinx} \\ $$$$\int\frac{−{d}\left({sinx}+{cosx}\right)}{\:\sqrt{\mathrm{1}−\mathrm{1}+{sin}\mathrm{2}{x}}} \\ $$$$\int\frac{−{d}\left({sinx}+{cosx}\right)}{\:\sqrt{\left({sinx}+{cosx}\right)^{\mathrm{2}}…
Question Number 116436 by mnjuly1970 last updated on 04/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\:\mathrm{0}} ^{\:\:\infty} \:\:\left(\frac{{sin}\left({x}\right).{sin}\left(\mathrm{2}{x}\right)}{{x}}\right)\:{dx}\:=???\: \\ $$$$\:\:\:\:\:\:\:\:\:…\:{m}.{n}.\mathrm{1970}… \\ $$$$\: \\ $$$$ \\…
Question Number 116427 by bemath last updated on 04/Oct/20 $$\:\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} \\…