Question

Integrate (x^2-4)/x * dx

Answer 1

Write
\[
\frac{x^2+4}x=x+\frac 4 x
\]
It is easy now to integrate

Answer 2

The integral is
\[

\frac{x^2}2 +4 \ln|x| +C
\]

Answer 3

Change the + 4ln|x| to - 4ln|x|
I misread the problem.

Answer 4

\[
\int \frac{x^2-4}x dx\int x -4 \frac{1}x dx=\frac {x^2}2 - 4\ln|x| + C


\]