Question Detail

First, integrate the expression (2x+1)/x:∫ (2x+1)/x dx = ∫ (2 + 1/x) dx = 2x + ln|x|.Now, evaluate the definite integral from a to 3a:[2x + ln|x|]a3a = (2(3a) + ln(3a)) - (2a + ln(a))= 6a + ln(3a) - 2a - ln(a)= (6a - 2a) + (ln(3a) - ln(a))= 4a + ln(3a/a)= 4a + ln(3).(Note: The original document's integral lower bound was OCR'd as '2', but 'a' is assumed to match the options provided, which is a common practice in such questions.)