∫dx⼀根号下1+x-x^2dx

∫dx/根号下1+x-x^2dx请问红线处是怎么化的?
2025-04-29 01:49:19
推荐回答(1个)
回答1:

1+x-x^2
=5/4-(x-1/2)^2
let
x-1/2 = (√5/2)sinu
dx =(√5/2)cosu du
∫dx/√(1+x-x^2)
=∫(√5/2)cosu du/[(√5/2)cosu]
=∫ du
=u +C
=arcsin[(2x-1)/√5] + C