Find the integral of (1/x) dx.

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Question: Find the integral of (1/x) dx.

Options:

Correct Answer: ln

Solution:

The integral of (1/x) is ln|x| + C, where C is the constant of integration.

Find the integral of (1/x) dx.

Find the integral of (1/x) dx.

Step 1: Identify the function you want to integrate, which is (1/x).
Step 2: Recall the rule for integrating (1/x), which states that the integral of (1/x) is the natural logarithm of the absolute value of x.
Step 3: Write down the result of the integral as ln|x|.
Step 4: Add the constant of integration, C, to the result, since the integral can have many possible values depending on the constant.
Step 5: Combine the results to get the final answer: ln|x| + C.

Integration of Rational Functions – Understanding how to integrate functions of the form 1/x, which leads to the natural logarithm.
Constant of Integration – Recognizing the importance of including the constant of integration (C) in indefinite integrals.