I'm having trouble understanding part of this answer. I know the answer is 1/6 ln (3x^2+6x-2)+C but I don't understand where the 1/6 ln comes from. Can anyone explain? Math lab closed before I got off work. Thanks.
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∫(x+1)/(3x^2+6x-2) dx , let u = 3x^2+6x-2 ---> du = 6(x+1)dx , so you can integrate
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-∫(x + 1)/(3x^2 + 6x - 2) dx
u = 3x^2 + 6x - 2
du/6 = (x + 1) dx
-1/6*∫du/u = -1/6*ln|3x^2 + 6x - 2| + C
u = 3x^2 + 6x - 2
du/6 = (x + 1) dx
-1/6*∫du/u = -1/6*ln|3x^2 + 6x - 2| + C