What is the antiderivative of ${ln x}^{3}$ $ln x^3$ ?

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Answer 1 · 2016-09-12T17:43:49

It is $3 (x ln x - x) + C$ $3(xlnx-x) +C$

Note that $ln (x^{3}) = 3 ln x$ $ln(x^3) = 3 lnx$ , so

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

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

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What is the antiderivative of lnx3ln x^3?