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Integral of 2x dx /(2x-2)
Let 2x=u
2 dx = du
dx = (1/2) du
Integral of 2x dx /(2x-2) = Integral of (1/2) u du / (u-2)
= Integral of 1/2 [ (u-2+2) / (u-2)] dx
= Integral of 1/2 [ 1+ 2/(u-2)] dx
= u/2 + (1/2) 2 ln(u-2) + C
= u/2 + ln(u-2) + C
= (2x/2) + ln(2x-2) + C
= x + ln(2x-2) + C
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