不定积分：

分部积分取 $u=\ln x,\ dv=dx$，则 $du=dx/x,\ v=x$：

$$\int \ln x\,dx=x\ln x-\int 1\,dx=\boxed{x\ln x-x+C}.$$

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英文解析

Using integration by parts with $u=\ln x$ and $dv=dx$, we have $du=dx/x$and $v=x$:

$$\int \ln x\,dx=x\ln x-\int 1\,dx=\boxed{x\ln x-x+C}.$$