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z-3-5z-10-dz-




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

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