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Category: Integration

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

Question Number 83960 by john santu last updated on 08/Mar/20 $$\int\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$ Commented by mathmax by abdo last updated on 08/Mar/20 $${I}\:=\int\:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −{x}}}{dx}\:\Rightarrow\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{2}{x}−\mathrm{1}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}}…

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

Question Number 18396 by Joel577 last updated on 20/Jul/17 $$\int\:\sqrt{\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\left({x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }}\:\:{dx} \\ $$ Answered by b.e.h.i.8.3.417@gmail.com last updated on 20/Jul/17 $$\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\left({x}^{\mathrm{2}} +{x}\right)^{\mathrm{2}}…

x-2-20-xsin-x-5cos-x-2-dx-

Question Number 83923 by jagoll last updated on 08/Mar/20 $$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{20}}{\left(\mathrm{xsin}\:\mathrm{x}+\mathrm{5cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last updated on 08/Mar/20 $$\Rightarrow\mathrm{xsin}\:\mathrm{x}+\mathrm{5cos}\:\mathrm{x}\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{25}}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{5}}\right)\right)…