令 √x-1=tx=(t+1)² dx=2(t+1)dt∫cos(√x-1)dx=∫2(t+1)costdt=∫2tcostdt+∫costdt∫2tcostdt=∫2tdsint=2tsint-2∫sintdt=2tsint+2cost原式=2tsint+2cost+sint+C=(2t+1)sint+2cost+C=(2√x-1)sin(√x-1)+2co...