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## Homework Statement

The problem that we have been given is to integrate the following: ∫( [itex]\frac{4}{2x-1}[/itex] )dx

## Homework Equations

I understand that the when [itex]\frac{a}{ax+b}[/itex] is integrated, the result is ln(ax+b) + C.

## The Attempt at a Solution

I have been told I need to make the numerator the same as the integer infront of the x term of the denominator (2) so that the equation meets the format to be [itex]\frac{a}{ax+b}[/itex], where a = 2 and b = -1. My lecturer informed me that I should change the 4 of the numerator from 4 to 2 and then place a 2 infront of the integral so that it looks like the following:

2∫([itex]\frac{2}{2x-1}[/itex]).

What I cant understand is why the (2x-1) term doesn't now become (x-0.5) if the 2 at the front of the integral means that the statement will be multiplied by 2, as the top is essentially multiplied by 2 but not the bottom. I may have missed something completely obvious here but this is bugging me slightly.

Thanks