求下列不定积分： (1)∫[(1+2x)/(x2+x)]dx； (2)∫[(x+3)/(x2+2x+5)]dx

求下列不定积分：
(1)∫[(1+2x)/(x²+x)]dx；
(2)∫[(x+3)/(x²+2x+5)]dx
【正确答案】：(1)∫[(1+2x)/(x²+x)]dx=∫[(1+x+x)/x(x+1)]dx =∫[1/x/1/(x+1)]dx =ln|x|+In|x+1|+C =ln|x²+x|+C (2)∫[(x+3)/(x²+2x+5)]dx=∫{[(x+1)+2]/[(x+1)²+4]}dx =∫(x+1)/[(x+1)²+4]dx+∫2/[(x+1)²+4]dx =1/2∫ 1/[(x+1)²+4]d[(x+1)²+4]+∫1/1+[(x+1)/2]²d(x+1)/2 =1/2ln[(x+1)²+4]+arctan[(x+1)/2]+C．