∫1/[x*(x^10+2)]dx

令u=x^10,du=10x^9 dx = 10u/x dx,dx = x/(10u) du∫dx/[x(x^10+2)]= (1/10)∫du/[u(u+2)] du= (1/20)∫2/[u(u+2)] du= (1/20)∫[(u+2)-u]/[u(u+2)] du= (1/20)∫[1/u - 1/(u+2)] du= (1/20)[∫du/u - ∫d(u+2)/(u+2)]= (1/20)[ln|u| - ln|u+2|] + C= (1/20)ln|x^10| - (1/20)ln|x^10+2| + C= (1/2)ln|x| - (1/20)ln|x^10+2| + C