求x除以根号下5+x-x^2的不定积分

∫ x/√(5 + x - x²) dx
= ∫ x/√[21/4 - (x - 1/2)²] dx
令x - 1/2 = (√21/2)sinz,dx = (√21/2)cosz dz
原式 = ∫ [1/2 + (√21/2)sinz]/|(√21/2)cosz| * [√(21/2)cosz dz]
= z/2 - (√21/2)cosz + C
= (1/2)arcsin[(2x - 1)/√21] - (√21/2) * 2√(5 + x - x²)/√21 + C
= (1/2)arcsin[(2x - 1)/√21] - √(5 + x - x²) + C