Finding the general antiderivative of a sum involving e^x and 1/x

Split the integral using linearity: $\int \left(7e^x - \frac{4}{x}\right)dx = 7\int e^x\,dx - 4\int \frac{1}{x}\,dx$. This lets us antidifferentiate each term separately using known rules.

Since $\int e^x\,dx = e^x$ and $\int \frac{1}{x}\,dx = \ln|x|$, we get $7e^x - 4\ln|x|$. Adding the arbitrary constant of integration gives the general antiderivative $F(x) = 7e^x - 4\ln|x| + C$.