变限积分的无穷小阶

对于

$$ \int_{\phi(x)}^{\varphi(x)}f(x){\rm d}x $$

其中 $\varphi(x)$、$\phi(x)$、$f(x)$ 的无穷小阶数分别是 $n_1$、$n_2$、$m$ ,则该变限积分的无穷小阶数等于

$$ \min\\{n_1,n_2\\}\times m+阶数\\{\varphi(x)-\phi(x)\\} $$

例题:

$$ \int_{x}^{\sin x}(e^{t^2}-1){\rm d}t $$

阶数为 $1\times2+3=5$

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