求下列不定积分： (1)∫dx/[2x+√(x+1)] (2)∫√(ex-1)dx．

求下列不定积分：
(1)∫dx/[2x+√(x+1)]
(2)∫√(e^x-1)dx．
【正确答案】：(1)令√(x+1)=t，则x=t²-1，dx=2tdt， ∫dx/[2+√(x+1)] =∫[2t/(2+t)]dt =2∫[(t+2-2)/(2+t)]dt =2∫[1-2/(2+t)]dt =2[t-2ln|2+t|]+C =2√(x+1)-4ln[2+√(x+1)]+C． (2)令√(e^x-1)=t，则x=ln(t²+1)，dx=2t/(t²+1)dt ∫√(e^x-1)dx =∫[t•2t/(t²+1)]dt =2∫[(t²+1-1)/(t²+1)]dt =2∫[1-1/(t²+1)dt =2(t-arctant)+C =2[√(e^x-1)-arctan√(e^x-1)]+C．