Question Number 101285 by student work last updated on 01/Jul/20
$$\int\frac{\left(\mathrm{x}^{\mathrm{m}} −\mathrm{x}^{\mathrm{n}} \right)}{\:\sqrt{\mathrm{x}}}\mathrm{dx}=? \\ $$
Commented by bobhans last updated on 01/Jul/20
$$\int\:\left({x}^{{m}−\frac{\mathrm{1}}{\mathrm{2}}} \:−\:{x}^{{n}−\frac{\mathrm{1}}{\mathrm{2}}} \right)\:{dx}\:=\:\frac{\mathrm{2}{x}^{{m}+\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}{m}+\mathrm{1}}\:−\:\frac{\mathrm{2}{x}^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{2}{n}+\mathrm{1}}\:+\:{c} \\ $$