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By substitution, $a=\ln x$.

By parts integration, when we let $u(x)=\frac{1}{x}$, where $u(x)$ is the integrated function, and we let $v^{\prime }(x)=\ln x$, where $v^{\prime }(x)$ is the differentiated function.

By substitution, $a=\frac{1}{x}$.

By factorization into $\int \frac{1}{x}\mathrm{d}x\cdot \int \frac{1}{\ln x}\mathrm{d}x$.