Answer: (1/2)ln|(x-1)/(x+1)| + C.
- A (1/2)ln|(x-1)/(x+1)| + C
- B ln|x-1| + C
- C (1/2)ln|(x+1)/(x-1)| + C
- D ln|x²-1| + C
Correct answer: A. (1/2)ln|(x-1)/(x+1)| + C
Explanation: 1/((x-1)(x+1)) = 1/2 × [1/(x-1) - 1/(x+1)]. Integrate: (1/2)[ln|x-1| - ln|x+1|] = (1/2)ln|(x-1)/(x+1)| + C.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.