Question Number 483 by 13/NaSaNa(N)056565 last updated on 25/Jan/15
$$\int\frac{\mathrm{1}}{\:\sqrt{{x}−\mathrm{1}}}{dx} \\ $$$$ \\ $$
Answered by 123456 last updated on 12/Jan/15
$$\int\frac{{dx}}{\:\sqrt{{x}−\mathrm{1}}} \\ $$$${u}={x}−\mathrm{1} \\ $$$${du}={dx} \\ $$$$\int\frac{{du}}{\:\sqrt{{u}}}=\int{u}^{−\mathrm{1}/\mathrm{2}} {du}=\frac{\mathrm{1}}{\mathrm{1}/\mathrm{2}}{u}^{\mathrm{1}/\mathrm{2}} +{c} \\ $$$$=\mathrm{2}\sqrt{{u}}+{c}=\mathrm{2}\sqrt{{x}−\mathrm{1}}+{c} \\ $$