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worty [1.4K]
3 years ago
6

What would be the u to usub and what would be the steps to solving this integral?

Mathematics
1 answer:
shutvik [7]3 years ago
3 0

Presumably, ln⁵(<em>x</em>) is the same as (ln(<em>x</em>))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(<em>x</em>)))))).

Then substituting <em>u</em> = ln(<em>x</em>) and d<em>u</em> = d<em>x</em>/<em>x</em> gives

\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}

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