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Question Number 6737 by FilupSmith last updated on 19/Jul/16

$$\mathrm{If}z\left(x\right)\mathrm{is}\mathrm{a}\mathrm{complex}\mathrm{function},$$$$\mathrm{is}\mathrm{the}\mathrm{following}\mathrm{true}:$$$$\int zdx=\int \mathrm{\Re }\left(z\right)dx+i\int \mathrm{\Im }\left(z\right)dx$$

Commented by prakash jain last updated on 19/Jul/16

$$\mathrm{Yes}.\mathrm{Since}i\mathrm{is}\mathrm{simply}\mathrm{a}\mathrm{constant}.$$$$\mathrm{For}\mathrm{example}$$$$\int (2x+{ix}^2)\mathrm{d}x=\int 2xdx+i\int x^2\mathrm{d}x$$

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