Antiderivative of log(x) without PartsI understand how the antiderivative of log(x) can be obtained by...
Antiderivative of log(x) without Parts
I understand how the antiderivative of log(x) can be obtained by Integration by Parts (i.e. product rule), but I was wondering how-if at all- it could be obtained only using sum/difference rule and substitution/chain rule.
Answer & Explanation
This may not necessarily be what you're looking for, but I got a kick out of it so I figured I'd share. We may evaluate the antiderivative by using integration by parts indirectly.
We seek the integral .
We set to get .
Integration by parts gives which is .
Choosing , .