求不定积分∫ dx/(a^2-x^2)
问题描述:
求不定积分∫ dx/(a^2-x^2)
答
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