1/[(x+1)*(x-1)^5)^(1/3)]的积分
问题描述:
1/[(x+1)*(x-1)^5)^(1/3)]的积分
答
∫ dx / [ (x+1) (x-1)^5 ] ^(1/3)= 1/2 ∫ [(x-1)/(x+1)] ^(-5/3) * 2/(x+1)² dx= 1/2 ∫ [(x-1)/(x+1)] ^(-5/3) d [(x-1)/(x+1)]= -3/4 [(x-1)/(x+1)] ^(-2/3) +C