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x-2-x-3-5-dx-




Question Number 7798 by Tawakalitu. last updated on 16/Sep/16
∫(x^2 /( (√(x^3  + 5)))) dx
$$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{3}} \:+\:\mathrm{5}}}\:{dx} \\ $$
Commented by sou1618 last updated on 16/Sep/16
(d/dx)((√(x^3 +5)))=((3x^2 )/(2(√(x^3 +5))))    ∫(x^2 /( (√(x^3 +5))))dx=(2/3)∫((3x^2 )/(2(√(x^3 +5))))dx     =(2/3)(√(x^3 +5))+C
$$\frac{{d}}{{dx}}\left(\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}\right)=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}} \\ $$$$ \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}{dx}=\frac{\mathrm{2}}{\mathrm{3}}\int\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}{dx} \\ $$$$\:\:\:=\frac{\mathrm{2}}{\mathrm{3}}\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}+{C} \\ $$
Commented by Tawakalitu. last updated on 16/Sep/16
Wow, thank you sir. i really appreciate.
$${Wow},\:{thank}\:{you}\:{sir}.\:{i}\:{really}\:{appreciate}. \\ $$

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