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完善不定积分的解法示例,添加变量还原步骤
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content/post/courses/calculus/indefinite-integral/index.md

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@@ -78,6 +78,12 @@ I &= \int \sqrt{1 - \sin^2 t} \cos t \mathrm{d}t \\
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\end{aligned}
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$$
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记得变量还原, 由 $x = \sin t$ 可得 $t = \arcsin x$, 又因为 $\sin 2t = 2 \sin t \cos t = 2x \sqrt{1 - x^2}$, 故
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$$
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I = \cfrac{1}{2} \arcsin x + \cfrac{1}{2} x \sqrt{1 - x^2} + C
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$$
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### 练习
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1. $ \displaystyle \int \sqrt{4 - x^2} dx $

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