※ 引述《bitchdog (上吧傑尼龜)》之銘言：
: x^2
: ∫ t^2g(t)dt=x^6(x^2+1), then g(x)=?
: 0
等號兩邊對 x 微分
(2x)((x^2)^2)(g(x^2)) = (6)(x^5)(x^2 + 1) + (x^6)(2x)
(2)(x^5)(g(x^2)) = (8)(x^7) + (6)(x^5)
(g(x^2)) = (4)(x^2) + 3
令 y = x^2 則 g(y) = 4y + 3 => g(x) = 4x + 3
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