Question

求不定积分：分子是一,分母是X乘以根号(2X+1)

Answer 1

令根号2x+1 =t x=（t^-1)/2 原式=∫t/((t^-1)/2 *t)dt =∫2/(t-1)(t+1) dt = -∫1/(t+1) -1/(t-1) dt =

ln((t+1)/(t-1)) +c

故原式=- ln ( (根号(2x+1) +1)/(根号(2x+1) -1) ) +c