令x²/(x+2)³=A/(x+2)+B/(x+2)²+C/(x+2)³解得A=1,B=-4,C=4原式=∫dx/(x+2) - 4∫dx/(x+2)² + 4∫dx/(x+2)³=ln|x+2| + 4/(x+2) - 2/(x+2)² + C=(4x+6)/(x+2)² + ln|x+2| + C
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