Question Number 6737 by FilupSmith last updated on 19/Jul/16
$$\mathrm{If}\:{z}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{function}, \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{true}: \\ $$$$\int{zdx}=\int\Re\left({z}\right){dx}+{i}\int\Im\left({z}\right){dx} \\ $$
Commented by prakash jain last updated on 19/Jul/16
$$\mathrm{Yes}.\:\mathrm{Since}\:{i}\:\mathrm{is}\:\mathrm{simply}\:\mathrm{a}\:\mathrm{constant}. \\ $$$$\mathrm{For}\:\mathrm{example} \\ $$$$\int\left(\mathrm{2}{x}+{ix}^{\mathrm{2}} \right)\mathrm{d}{x}=\int\mathrm{2}{xdx}+{i}\int{x}^{\mathrm{2}} \:\mathrm{d}{x} \\ $$