Question:
If \( f'(x) = x^{-1} \), then find \( f(x) \)
If \( f'(x) = x^{-1} \), then find \( f(x) \)
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The integral of \( x^{-1} \) is \( \log |x| + c \); include absolute value for domain consistency.
Updated On: Nov 11, 2025
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Solution and Explanation
Given: \( f'(x) = \frac{1}{x} \).
Integrate:
\[ f(x) = \int \frac{1}{x} \, dx = \log |x| + c, \text{where } c \text{ is the constant of integration.} \] Answer: \( f(x) = \log |x| + c \).
Integrate:
\[ f(x) = \int \frac{1}{x} \, dx = \log |x| + c, \text{where } c \text{ is the constant of integration.} \] Answer: \( f(x) = \log |x| + c \).
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