Problem 7
Question
Give the antiderivatives of \(1 / x\)
Step-by-Step Solution
Verified Answer
Answer: The antiderivative of the given function \(\frac{1}{x}\) is \(F(x) = \ln |x| + C\).
1Step 1: Identify the given function
The function given in this problem is \(f(x) = \frac{1}{x}\).
2Step 2: Find the antiderivative
The antiderivative of \(f(x) = \frac{1}{x}\) is the natural logarithm function, which is commonly written as \(\ln |x|\). Remember that when finding antiderivatives, there is always an arbitrary constant of integration, denoted by \(C\). So, the antiderivative of \(f(x)\) is:
$$
F(x) = \ln |x| + C
$$
3Step 3: Final Answer
The antiderivative of the given function, \(1 / x\), is:
$$
F(x) = \ln |x| + C
$$
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