Category: Integration

Question Number 86302 by john santu last updated on 28/Mar/20 $$\int \frac{dx}{(x^2+1)\sqrt{x^2+4}}=?$$ Commented by abdomathmax last updated on 28/Mar/20 $${I}\:=\int\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} \:+\mathrm{4}}}\:{changement}\:{x}\:=\mathrm{2}{sh}\left({t}\right)\:{give}…

Question Number 86269 by M±th+et£s last updated on 27/Mar/20 $$\int \frac{{sec}^2\left(x\right)}{{(tan\left(x\right)-1)}^4(tan\left(x\right)-2)}dx$$ Commented by john santu last updated on 28/Mar/20 $$u=\tan x-2$$$$\Rightarrow\:\int\:\frac{{du}}{\left({u}+\mathrm{1}\right)^{\mathrm{4}}…

Question Number 86254 by sakeefhasan05@gmail.com last updated on 27/Mar/20 $$\int \sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\dots \dots .}}}}\mathrm{dx}$$ Answered by TANMAY PANACEA. last updated on 27/Mar/20 $$y=\sqrt{x\sqrt{x\sqrt{x\sqrt{x\dots \mathrm{\infty }}}}}$$$$y=\sqrt{xy}$$$${y}^{\mathrm{2}}…

Question Number 86247 by M±th+et£s last updated on 27/Mar/20 $${\int }_0^8{\int }_0^{x^{\frac{2}{3}}}\sqrt{x^2+y^2+1}dydx$$ Commented by mathmax by abdo last…

Question Number 151756 by Integrals last updated on 22/Aug/21 Commented by MJS_new last updated on 22/Aug/21 $$\int ({\cot }^{1/4}\beta +{\tan }^{1/4}\beta )d\beta =$$$$\:\:\:\:\:\left[{t}=\mathrm{tan}^{\mathrm{1}/\mathrm{4}} \:\beta\:\rightarrow\:{d}\beta=\frac{\mathrm{4}{t}^{\mathrm{3}} }{{t}^{\mathrm{8}} +\mathrm{1}}{dt}\right] \…