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