How do you use integration by parts to find $\int ln (x) d x$ $intln(x) dx$ ?

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Answer 1 · 2014-09-22T22:55:48

By Integration by Parts: $\int u d v = u v - \int v d u$ $int udv=uv-int vdu$ ,

Let $u = ln x$ $u=lnx$ and $d v = d x$ $dv=dx$ .
$\Rightarrow d u = \frac{d x}{x}$ $Rightarrow du=dx/x$ and $v = x$ $v=x$

$\int ln x d x = x ln x - \int d x = x ln x - x + C$ $int lnx dx=xlnx-int dx=xlnx-x+C$ ,

where C is a constant.

How do you use integration by parts to find ∫ln(x)dxintln(x) dx?