Question Number 85323 by sahnaz last updated on 20/Mar/20
$$\int\frac{\mathrm{z}−\mathrm{3}}{\mathrm{5z}−\mathrm{10}}\mathrm{dz} \\ $$
Answered by MJS last updated on 20/Mar/20
$$\int\frac{{z}−\mathrm{3}}{\mathrm{5}{z}−\mathrm{10}}{dz}=\frac{\mathrm{1}}{\mathrm{5}}\int\frac{{z}−\mathrm{3}}{{z}−\mathrm{2}}{dz}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{5}}\int{dz}−\frac{\mathrm{1}}{\mathrm{5}}\int\frac{{dz}}{{z}−\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{5}}{z}−\frac{\mathrm{1}}{\mathrm{5}}\mathrm{ln}\:\mid{z}−\mathrm{2}\mid\:+{C} \\ $$