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First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int x \ln (1 + x) dx $

$\frac{1}{2}\left(x^{2}-1\right) \ln (1+x)-\frac{1}{4} x^{2}+\frac{1}{2} x+\frac{3}{4}+C$

Integration Techniques

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Campbell University

Harvey Mudd College

Baylor University

Boston College

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