I'm trying to figure out how to Integrate a function like that without the use of $u-$substitution. Would really appreciate some help here!

$$\int\ln^2 x\,dx$$

Thanks in advance!


Integrate by parts: $$\int \ln^2 x\,dx = x\ln^2 x-\int 2\ln x\,dx = x\ln^2 x-2\left(x\ln x-x+C\right), C \in \mathbb{R}.$$

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  • $\begingroup$ Gibbs, how would you go on about solving it with $u$-substitution? $\endgroup$ – user472288 May 8 '18 at 15:22
  • $\begingroup$ I do not know. Even if I try a substitution I end up using integration by parts. $\endgroup$ – Gibbs May 8 '18 at 18:07

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