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Integration by parts treats ln x as ln x times 1. What antiderivative results?

Ax ln x + x + C
Bx/ln x + C
Cx ln x − x + C
D(ln x)/x + C
Answer & Solution
Correct answer: C. x ln x − x + C
Writing ln x as ln x · 1 and taking u = ln x gives x ln x − ∫dx = x ln x − x.
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