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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.


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