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Evaluate: int(logx)/x\ dx...

Evaluate: `int(logx)/x\ dx`

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To evaluate the integral \(\int \frac{\log x}{x} \, dx\), we will use the method of substitution. Let's go through the steps one by one. ### Step-by-Step Solution: 1. **Substitute \( t = \log x \)**: \[ t = \log x \] ...
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Knowledge Check

  • int(logx)/x^2dx =

    A
    `1/x(logx+1)`
    B
    `-1/x (log x+1)`
    C
    `1/x (log x-1)`
    D
    `log (x+1)`

  • int(logx)/(x^3)dx=

    A
    `(1)/(4x^2)(2logx-1)+c`
    B
    `(-1)/(4x^2)(2logx+1)+c`
    C
    `(1)/(4x^2)(2logx+1)+c`
    D
    `(1)/(4x^2)(1-2logx)+c`

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