用第一类换元积分法求下列不定积分

麻烦给个详细点的过程 谢谢
2025-04-16 12:33:08
推荐回答(1个)
回答1:

(1)
let

u=√x
2udu = dx
∫ [cos(√x -1)/(2√x) ] dx
=∫ [cos(u -1)/(2u) ] ( 2u du)
=∫ cos(u -1) du
=sin(u-1) + C
=sin(√x-1) + C
(2)
∫ dx/(x^2-4)
=(1/4)∫ [1/(x-2) - 1/(x+2)] dx
=(1/4)ln| (x-2)/(x+2)| + C