麻烦写下详细过程 拜托了
答:∫[x/(x^2+2x+2)]dx
=∫ {(x+1-1)/[(x+1)²+1]}dx
=∫{(x+1)/[(x+1)²+1]}d(x+1) - ∫ {1/[(x+1)²+1]} d(x+1)
=(1/2)∫ {1/[(x+1)²+1]} d[(x+1)²+1] - ∫ {1/[(x+1)²+1]} d(x+1)
=(1/2) ln [(x+1)²+1] -arctan(x+1)+C
= ln√(x²+2x+2) -arctan(x+1)+C