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

By substitution, $a=\sin x$.

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

By substitution, $t=\sin (\ln x)$.