关于不定积分的/>
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/14 01:15:19
关于不定积分的
![](http://img.wesiedu.com/upload/e/19/e19fd6bb7635c1e291931af8afced52b.jpg)
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![](http://img.wesiedu.com/upload/e/19/e19fd6bb7635c1e291931af8afced52b.jpg)
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![关于不定积分的/>](/uploads/image/z/7158291-51-1.jpg?t=%E5%85%B3%E4%BA%8E%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E7%9A%84%2F%3E)
令a=arcsinx
x=sina
cosa=√(1-x²)
dx=cosada
原式=∫a²cosada
=∫a²dsina
=a²sina-∫sinada²
=a²sina+2∫adcosa
=a²sina+2acosa-2∫cosada
=a²sina+2acosa-2sina+C
=x(arcsinx)²+2arcsinx*√(1-x²)-2x+C
x=sina
cosa=√(1-x²)
dx=cosada
原式=∫a²cosada
=∫a²dsina
=a²sina-∫sinada²
=a²sina+2∫adcosa
=a²sina+2acosa-2∫cosada
=a²sina+2acosa-2sina+C
=x(arcsinx)²+2arcsinx*√(1-x²)-2x+C