# How do you evaluate #int 1/(x-3)dx# from 1 to 4?

This transforms the integral as follows:

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To evaluate the integral of 1/(x-3)dx from 1 to 4, we need to find the antiderivative of the function 1/(x-3) with respect to x, and then evaluate it at the upper limit (4) and subtract the value of the antiderivative at the lower limit (1).

The antiderivative of 1/(x-3) is ln|x-3|.

So, integrating 1/(x-3)dx from 1 to 4:

∫(1/(x-3))dx from 1 to 4 = [ln|x-3|] evaluated from 1 to 4 = [ln|4-3|] - [ln|1-3|] = [ln|1|] - [ln|-2|] = ln(1) - ln(2) = 0 - ln(2) = -ln(2)

Therefore, the value of the integral of 1/(x-3)dx from 1 to 4 is -ln(2).

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