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Category: Integration

sec-2-x-tan-x-1-4-tan-x-2-dx-

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

x-x-x-x-dx-

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

x-2-1-x-2-1-1-1-x-4-dx-

Question Number 86246 by Rio Michael last updated on 27/Mar/20 $$\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx}\:=\:? \\ $$ Answered by TANMAY PANACEA. last updated on 27/Mar/20 $$\int\frac{\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}}…

Question-151780

Question Number 151780 by Tawa11 last updated on 23/Aug/21 Answered by puissant last updated on 23/Aug/21 $${Q}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{arctanx}}{{x}}{dx} \\ $$$${arctanx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}…

Question-151756

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