What is the integral `int -sin(ln(x))/x dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The integral `int -sin(ln(x))/x dx` has to be determined.

If `ln x = y` , `dy = dx/x`

`int -sin(ln(x))/x dx`

=> `int -sin y dy`

=> `cos y + C`

substituting `y = ln x`

=> `cos (ln (x)) + C`

The integral `int -sin(ln(x))/x dx = cos (ln (x)) + C`

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