Question

What is the antiderivative of `ln x^3`?

Answer 1

It is `3(xlnx-x) +C`

Explanation:

Note that `ln(x^3) = 3 lnx`, so

ihe antiderivative of `ln(x^3)` is `3` times the antiderivative of `lnx`.

The antiderivative of `lnx` can be found by integration by parts to be `xlnx-x`.

Here is one explanation of that result: https://socratic.org/questions/how-do-i-find-the-integral-in-x-d-x?source=search

I am sure there are others on Socratic, the question has been asked more that once.