Question

What is the antiderivative of `2/x`?

Answer 1

`2lnabs(x)+C`

Explanation:

Begin by writing the problem in mathspeak:
`int2/xdx`

We know that `int1/xdx=lnabs(x)+C`; so how can we simplify `int2/xdx` to `int1/xdx`? Well, there's a rule for integrals that says: `intcxdx=cintxdx`; in other words, we can pull constants out of the integral. Because `2` is a constant, we can bring it out:
`=2int1/xdx`

And applying the antiderivative of `1/x`, we have:
`2(lnabs(x)+C)=2lnabs(x)+C->`(note that `2C` is just another constant, so we can write it as `C`)