令x = 3 * sint，dx = 3 * cost dt
∫ x^2√(9 - x^2) dx
= ∫ 9 * sin^2(t) * 3 * cost * 3 * cost dt
= 81∫ (sint cost)^2 dt
= 81∫ (1/2 * sin(2t))^2 dt
= (81/4)∫ (1 - cos(4t))/2 dt
= (81/8)(t + (1/4)sin(4t)) + C
将sint = x/3 和 cost = √(9 - x^2)/3 都代入
得结果为(1/8)[ x(2x^2 - 9)√(9 - x^2) + 81arcsin(x/3) ] + C
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