Question Detail

Since the degree of the numerator (2) is greater than the degree of the denominator (1), perform polynomial long division or algebraic manipulation. We can rewrite x² as (x² - 1 + 1). So, x²/(x+1) = (x²-1+1)/(x+1) = ((x-1)(x+1) + 1)/(x+1) = (x-1) + 1/(x+1). Now, integrate the simplified expression: ∫ ((x-1) + 1/(x+1)) dx = ∫ x dx - ∫ 1 dx + ∫ 1/(x+1) dx. This integrates to x²/2 - x + ln|x+1| + C.