求不定积分∫dx/(a+x)(a-x)原式=∫dx/(a+x)(a-x)=1/2a*∫[1/(a+x)+1/(a-x)]dx=1/2a*(ln|a+x|+ln|a-x|)+C=ln|a²-x²|/2a+C中的1/2a*是怎么来的
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![求不定积分∫dx/(a+x)(a-x)原式=∫dx/(a+x)(a-x)=1/2a*∫[1/(a+x)+1/(a-x)]dx=1/2a*(ln|a+x|+ln|a-x|)+C=ln|a²-x²|/2a+C中的1/2a*是怎么来的](/uploads/image/z/10137093-69-3.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E2%88%ABdx%2F%28a%2Bx%29%28a-x%29%E5%8E%9F%E5%BC%8F%3D%E2%88%ABdx%2F%28a%2Bx%29%28a-x%29%3D1%2F2a%2A%E2%88%AB%5B1%2F%28a%2Bx%29%2B1%2F%28a-x%29%5Ddx%3D1%2F2a%2A%28ln%7Ca%2Bx%7C%2Bln%7Ca-x%7C%29%2BC%3Dln%7Ca%26%23178%3B-x%26%23178%3B%7C%2F2a%2BC%E4%B8%AD%E7%9A%841%2F2a%2A%E6%98%AF%E6%80%8E%E4%B9%88%E6%9D%A5%E7%9A%84)
求不定积分∫dx/(a+x)(a-x)原式=∫dx/(a+x)(a-x)=1/2a*∫[1/(a+x)+1/(a-x)]dx=1/2a*(ln|a+x|+ln|a-x|)+C=ln|a²-x²|/2a+C中的1/2a*是怎么来的
求不定积分∫dx/(a+x)(a-x)
原式=∫dx/(a+x)(a-x)=1/2a*∫[1/(a+x)+1/(a-x)]dx=1/2a*(ln|a+x|+ln|a-x|)+C=ln|a²-x²|/2a+C中的1/2a*是怎么来的
求不定积分∫dx/(a+x)(a-x)原式=∫dx/(a+x)(a-x)=1/2a*∫[1/(a+x)+1/(a-x)]dx=1/2a*(ln|a+x|+ln|a-x|)+C=ln|a²-x²|/2a+C中的1/2a*是怎么来的
是简单恒等变换得来的:
1/[(a+x)(a-x)]
=[1/(2a)]·2a/[(a-x)(a+x)]
=[1/(2a)]·[(a-x)+(a+x)]/[(a+x)(a-x)]
=[1/(2a)]·{(a-x)/[(a+x)(a-x)]+(a+x)/[(a+x)(a-x)]}
=[1/(2a)]·[1/(a+x)+1/(a-x)].
积分部分,你应该明白,不重复了.
1/(a+x)(a-x)
=1/2a ×(2a)/(a+x)(a-x)
=1/2a [(a+x)+(a-x)]/(a+x)(a-x)
=1/2a [(a+x)/(a+x)(a-x) +(a-x)/(a+x)(a-x)]
=1/2a [1/(a-x) +1/(a+x)]
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求不定积分∫dx/(a+x)(a-x)原式=∫dx/(a+x)(a-x)=1/2a*∫[1/(a+x)+1/(a-x)]dx=1/2a*(ln|a+x|+ln|a-x|)+C=ln|a²-x²|/2a+C中的1/2a*是怎么来的