Ok, so if $f$ is a real function, then I know how to calculate $\int f(x) dx$.
If $f(x)$ is a complex-valued function, i.e. an expression that involves i, then $\int f(x) dx$ is calculated in the same way as before: I just treat $i$ as a constant.
However, now I am reading a book which writes integrals as $\int Re(f(x)) dx$ where $Re()$ denotes the real part of $f$.
And this, I don't understand. I don't know what the real part of $f$ is, so this expression seems to me impossible to calculate? The book also doesn't tell me how I can calculate this.
So how do I calculate this integral? In other words, how do I figure out what the real part of a function is? Or can the integral be calculated in another way?
Assuming that $x$ is a real number the $Re(f(x))$ is the real part of $f(x)$ which is the part of $f(x)$ which does not involve $i$
For example if you have $$f(x) = 3x^2 + 2ix^3$$
Then the real part of $f(x)$ is $$ Re(f) = 3x^2$$ and the integral is $$\int Re(f(x))dx = \int 3x^2 dx = x^3+C $$