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int (4x + 2)/(2x - 1) dx
= int [(2x - 1) + (2x - 1) + 2]/(2x - 1) dx
bagi masing-masing:
= int (1 + 1 + 2/(2x - 1)) dx
= x + x + ln|2x - 1| + c
= 2x + ln|2x - 1| + c
2x - 1
Misal U = 2x - 1 ⇒ du = 2dx ⇔ 2du = 4dx
Integral (4x + 2) = Integral (2 + 4/(2x - 1))dx
2x - 1 = 2x + integral 4dx/(2x-1)
= 2x + integral 2/u du
= 2x + 2ln I u I + C
= 2x + 2 ln I 2x - 1 I + C