How do you find the integral of 1/x?

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To find the integral of the function 1/x, we can utilize the concept of basic integration in calculus. The integral of 1/x is a well-known result and can be computed as follows:

The integral expression can be written mathematically as:

∫ (1/x) dx

The result of this integral is:

ln|x| + C

Where:

  • ln denotes the natural logarithm,
  • |x| indicates the absolute value of x, and
  • C is the constant of integration, which accounts for any constant value that could be added to the function.

To summarize:

  • When integrating 1/x, the integral yields ln|x| + C.
  • This result is valid for x ≠ 0.

Understanding this integral is foundational in calculus, particularly because it appears in various applications across mathematics, physics, and engineering. It’s also crucial for solving logarithmic equations and understanding growth rates within natural processes.

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