# What is the antiderivative of ln x^3?

Sep 12, 2016

It is $3 \left(x \ln x - x\right) + C$

#### Explanation:

Note that $\ln \left({x}^{3}\right) = 3 \ln x$, so

ihe antiderivative of $\ln \left({x}^{3}\right)$ is $3$ times the antiderivative of $\ln x$.

The antiderivative of $\ln x$ can be found by integration by parts to be $x \ln x - x$.

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.