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Okay, This question wants us to compute this integral
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. So to do this, we need to find
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a foreman or table that looks like this. But
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that's not gonna work out unless if we do some
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pre processing here. So well, it's factor out
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our common factor of X squared on the bottom here
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. And no, if we look at our table
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in the back of the book, we see this
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formula, which is exactly the form that are integral
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is in. We just have to flip some signs
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. So we get integral of D X over X
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squared times, negative three plus two X and now
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that's exactly in this form. So we just gotta
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value at this formula with our values of A and
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B. So So a is the constant term,
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which is negative three and B equals our term in
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front of the X, which is to So now
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we just need to plug into our formula which says
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that it's negative one divided by negative three times are
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variable x plus. See over a squared times the
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natural log of a plus b, u or B
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X. In this case divided by X plus c
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and then we can just do a little bit of
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simplification and get won over three X plus 2/9 times
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the natural log of two X minus three over X
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plus C, which is our final answer.