MathAnalysisCalculusIntegrals

Integration by parts

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Consider the following integral

$I = \int \frac{\ln(x)}{(1+x)^2} \ dx$ What is an equivalent expression for $I$ after solving the integral?

Select one option from the list

I = -\frac{\ln(x)}{x+1} + \ln \left| \frac{x}{x+1} \right| + C

I = \ln \left| \frac{x}{(x+1)^2} \right| + C

I = \frac{1}{x (1+x)^2} - \ln \left| \frac{x}{x+1} \right| + C

I = - \frac{x}{x+1} + \ln(x) + C

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