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The derivative of ln(x) is simply 1/x. The derivative of 1/u is du/u.
The integrals simply reverse this process. Many of the problems in this section will require the use of substitution to successfully complete the problem.
Question: Why does the integral of of 1/x have an absolute value?
Answer: 1/x has a slope for negative x values because the function exists there. As you can see below ln(x) does not exist for negative x values. With the absolute value, you can see that the slope of ln|x| now exists in the form of 1/x for negative and positive values.
Have logarithm blues, or do you forget any of the rules? Check this out.
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