CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The indefinite integral of 1/x with respect to x, for x > 0, is:
The integral of 1/x with respect to x is ln x plus a constant, because the derivative of ln x is 1/x. This is the standard exception to the power rule, which fails for the power minus one.
- Aln x + cCorrect
- B1/x² + c
- C−1/x² + c
- Dx ln x + c
Explanation
The standard formula is ∫(1/x) dx = ln|x| + c, since d/dx(ln x) = 1/x. The option −1/x² is the derivative of 1/x, not its integral, so it comes from differentiating instead of integrating.
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