How to evaluate the following integral? $$ \int_{0}^{1} \frac{\ln(1+x)}{x} dx .$$ I have expanded the numerator using Maclaurin series and the result is $$ \int_{0}^{1} \frac{x -\frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}+\ldots}{x}dx. $$ And I have found out that it is $ \pi^2/12 $. Is this correct?
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1Yeah that's right – user525966 Jun 01 '21 at 15:48
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2Yes, that is correct. – Gary Jun 01 '21 at 15:48