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This question tests the student's knowledge of the use of singular and plural pronouns, as well as the subjunctive. La gente (the people) is singular, so should be followed by a singular verb, as...

Here we can use integration by parts. Notice that ln(x) can be written as ln(x)1, so we can integrate 1 and differentiate ln(x).
Then using the formula int(uv') dx = uv - int(u'v) dx, we...