# Calc1.2

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errodom $\int \ln {x}dx\,$

In order to compute this integral, one must do integration by parts.
Recall that the formula for this method is $\int u\,dv=uv-\int v\,du\,$.

Let $u\,$ be $\ln x\,$ and let $dv\,$ be $dx\,$.
$du\,$ is then ${\frac {1}{x}}dx\,$, and $v\,$ is $x\,$.

Substituting all of this into the integration by parts formula, we arrive at this expression

$\int {\ln {x}\,dx}\ =x\ln x-\int {(x)\left({\frac {1}{x}}\right)\,dx}$

$=x\ln x-x\,$

$=x(\ln x-1)\,$

Note that this technique works for many integrals in a similar form.

Calculus