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Integral leading to the ln: reciprocal of a linear * ln of another linear:

Since we don't have any rules for this case of the log function appearing in the integral (we only have rules in which the log function appears in the result), we need to substitute for it:

Let

, and

.

In the original problem, we need to replace the combination

Combining these results, we have

, or with the Scalar Multiple rule,

Using the rule for integration involving the natural log, we get

Now we substitute for u to get a result in terms of x:

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