Question

用第一换元法求不定积分(1除以根号x-1)的解?

Answer 1

∫dx/√(x-1),令t=x-1,dt=dx
= ∫dt/√t
=∫t^(-1/2) dt
= t^(-1/2+1) / (-1/2+1) + C,积分基本定理∫x^n dx = x^(n+1) / (n+1),n为常数
= t^(1/2) / (1/2) + C
= 2√t + C
= 2√(x-1) + C,C为常数