What is the antiderivative of $ln x^(1/3)$ ?

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Answer 1 · 2016-02-19T01:07:27

Use integration by parts and simplify $lnx^(1/3)$ to $(1/3)lnx$

Let $u =(1/3) lnx$ and $dv=dx$

Then, $du=1/(3x)$ and $v=x$

Using the integration by parts formula ...

$uv-intvdu$

$x/3lnx-intx(1/(3x))dx$

Simplify ...

$(x/3)(lnx-1)+C$

hope that helped

What is the antiderivative of ln x^(1/3) ln x^(1/3)?