求不定积分（2+x-x^2)^1/2dx

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求不定积分（2+x-x^2)^1/2dx
求不定积分（2+x-x^2)^1/2dx

求不定积分（2+x-x^2)^1/2dx
令 x﹣1/2 = (3/2) sint,dx = (3/2) cost dt
| = ∫ (9/4) cos²t dt
= 9/8 ∫ (1+ cos2t) dt
= (9/8) { t + (1/2)sin2t } + C
= (9/8) arcsin(2x-1)/3 + (1/2) (x-1/2) √(2+x﹣x²) + C

积分:[(9/4)-(x-1/2)^2]^(1/2) dx
=sin^(-1)((x-1/2)/(3/2))
=sin^(-1)((2x-1)/3)

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