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What is the integral of 1/x? (2022)
What is the integral of 1/x? (2022)
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Practice Questions
1 question
Q1
What is the integral of 1/x? (2022)
ln
x
+ C
1/x + C
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The integral of 1/x is ln|x| + C.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the integral of 1/x? (2022)
Solution:
The integral of 1/x is ln|x| + C.
Steps: 6
Show Steps
Step 1: Understand that we want to find the integral of the function 1/x.
Step 2: Recall that the integral is the opposite of the derivative. We need to find a function whose derivative is 1/x.
Step 3: Remember that the derivative of the natural logarithm function, ln(x), is 1/x for x > 0.
Step 4: Since the function 1/x is defined for both positive and negative values of x (except at x = 0), we use the absolute value: ln|x|.
Step 5: Add a constant 'C' to the result because the integral can have many functions that differ by a constant.
Step 6: Conclude that the integral of 1/x is ln|x| + C.
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