Question Number 84126 by Roland Mbunwe last updated on 09/Mar/20
$$\int\frac{\mathrm{5}−{x}}{\mathrm{1}+\sqrt{\left({x}−\mathrm{4}\right)}}\boldsymbol{{dx}} \\ $$
Answered by MJS last updated on 09/Mar/20
$$−\int\frac{{x}−\mathrm{5}}{\mathrm{1}+\sqrt{{x}−\mathrm{4}}}{dx}=\int\left(\mathrm{1}−\sqrt{{x}−\mathrm{4}}\right){dx}= \\ $$$$={x}−\frac{\mathrm{2}}{\mathrm{3}}\left({x}−\mathrm{4}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +{C} \\ $$
Commented by MJS last updated on 09/Mar/20
$$−\frac{{x}−\mathrm{5}}{\mathrm{1}+\sqrt{{x}−\mathrm{4}}}×\frac{\mathrm{1}−\sqrt{{x}−\mathrm{4}}}{\mathrm{1}−\sqrt{{x}−\mathrm{4}}}=−\frac{\left({x}−\mathrm{5}\right)\left(\mathrm{1}−\sqrt{{x}−\mathrm{4}}\right)}{\mathrm{5}−{x}}= \\ $$$$=\mathrm{1}−\sqrt{{x}−\mathrm{4}} \\ $$