What is the indefinite integral of ln(ln(lnx))?

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What is the indefinite integral of $\ln(\ln(\ln(x))$? I came across this question somewhere and got curious as to what would be the solution. I know that the indefinite integral of $\ln(\ln(x))$ is $x \ln(\ln(x))-\operatorname{li}(x)+C$ and am familiar with introductory college level calculus. Do we have to use another special function?