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Question Number 121825 by bemath last updated on 12/Nov/20

  ∫ (dx/(x−4(√x))) ?

$$\:\:\int\:\frac{{dx}}{{x}−\mathrm{4}\sqrt{{x}}}\:? \\ $$

Commented by bemath last updated on 12/Nov/20

 ∫ (dx/( (√x) ((√x)−4))) dx = 2∫ ((d((√x)−4))/( (√x)−4))  = 2 ln ∣(√x)−4 ∣ + c

$$\:\int\:\frac{{dx}}{\:\sqrt{{x}}\:\left(\sqrt{{x}}−\mathrm{4}\right)}\:{dx}\:=\:\mathrm{2}\int\:\frac{{d}\left(\sqrt{{x}}−\mathrm{4}\right)}{\:\sqrt{{x}}−\mathrm{4}} \\ $$$$=\:\mathrm{2}\:\mathrm{ln}\:\mid\sqrt{{x}}−\mathrm{4}\:\mid\:+\:{c}\: \\ $$

Answered by Dwaipayan Shikari last updated on 12/Nov/20

∫(dx/( (√x)((√x)−4)))  =2∫(1/(2(√x))).(1/( (√x)−4))dx  =2log((√x)−4)+C

$$\int\frac{{dx}}{\:\sqrt{{x}}\left(\sqrt{{x}}−\mathrm{4}\right)} \\ $$$$=\mathrm{2}\int\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}.\frac{\mathrm{1}}{\:\sqrt{{x}}−\mathrm{4}}{dx} \\ $$$$=\mathrm{2}{log}\left(\sqrt{{x}}−\mathrm{4}\right)+{C} \\ $$

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