求不定积分x^2⼀(x+2)^3dx 用凑微分法应该如何解

2025-01-03 07:50:13
推荐回答(2个)
回答1:

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

回答2:

问题不详,无法解答