Menu Close

Cheap-x-x-x-dx-




Question Number 77089 by Dah Solu Tion last updated on 03/Jan/20
Cheap ⇊  ∫(√(x/( (√(x/( (√(x/(...)))))))))dx
$$\boldsymbol{{Cheap}}\:\downdownarrows \\ $$$$\int\sqrt{\frac{\boldsymbol{{x}}}{\:\sqrt{\frac{\boldsymbol{{x}}}{\:\sqrt{\frac{\boldsymbol{{x}}}{…}}}}}}\boldsymbol{{dx}} \\ $$$$ \\ $$$$ \\ $$
Commented by Tony Lin last updated on 03/Jan/20
y=(√(x/y))  y^2 =(x/y)  y=x^(1/3)   ∫ydx  =∫x^(1/3) dx  =(3/4)x^(4/3) +c
$${y}=\sqrt{\frac{{x}}{{y}}} \\ $$$${y}^{\mathrm{2}} =\frac{{x}}{{y}} \\ $$$${y}={x}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\int{ydx} \\ $$$$=\int{x}^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$$$=\frac{\mathrm{3}}{\mathrm{4}}{x}^{\frac{\mathrm{4}}{\mathrm{3}}} +{c} \\ $$
Commented by Dah Solu Tion last updated on 03/Jan/20
Nice one boss
$${Nice}\:{one}\:{boss} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *