Answer: -ln|x+2| + 2ln|x+3| + C.
- A -ln|x+2| + 2ln|x+3| + C
- B ln|x+2| + ln|x+3| + C
- C (x+1)/(x+2)(x+3) + C
- D 2ln|x+3| - ln|x+2| + C
Correct answer: A. -ln|x+2| + 2ln|x+3| + C
Explanation: Partial fractions: (x+1)/[(x+2)(x+3)] = A/(x+2)+B/(x+3). Setting x=−2: A=−1; x=−3: B=2. Integral = −∫dx/(x+2)+2∫dx/(x+3) = −ln|x+2|+2ln|x+3|+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.