| 一类三次无理函数积分的求解方法 |
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| 引用本文： | 陈翠玲,李明.一类三次无理函数积分的求解方法[J].数学学习,2010(6):41-45. |
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| 作者姓名： | 陈翠玲 李明 |
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| 作者单位： | [1]广西师范大学数学科学学院,广西桂林 541004 [2]桂林理工大学理学院,广西桂林 541004 |
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| 基金项目： | 基金项目：广西教育厅科研基金项目（200911LX53）}广西师范大学青年骨干教师基金项目（师政科技（2009）7）. |
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| 摘 要： | 设Pn(x)为n次多项式,a0≠0,m≥2且m∈N,得到形如∫Pn(x)ma0x3+a1x2+a2x+a3dx的三次无理函数积分可解的充要条件,且其解的形式为∫Pn(x)ma0x3+a1x2+a2x+a3dx=Qn-2(x).m(a0x3+a1x2+a2x+a3)m-1+C,其中Qn-2(x)为各项系数待定的(n-2)次多项式.运用待定系数法可求出Qn-2(x)的各项系数.
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| 关 键 词： | 无理函数 积分 充要条件 |
Antiderivative of Cubic Irrational Functions |
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| CHEN Cui Ling,LI Ming.Antiderivative of Cubic Irrational Functions[J].Studies In College Mathematics,2010(6):41-45. |
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| Authors: | CHEN Cui Ling LI Ming |
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| Institution: | 1. Department of Mathematics Science, Guangxi Normal University, Guilin, Guangxi, 541004, PRC, 2. College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, PRC. ) |
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| Abstract: | Let Pn（x） be a polynomial of degree n, a0≠0,m≥2abd m∈N . A necessary and sufficient condition is obtained which makes the following antiderivative formula holds ∫Pn（x）/m√（a0x3＋a1x3＋a2x＋a2 dx=Qx-2（x）·m√（a0x3＋a1x3＋a2x＋a3）^（m-1）＋C where Qn-2 （x） is a polynomial of degree n - 2. The coefficients of Qn-2 （x） can be found by the method of undermined coefficients. |
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| Keywords: | irrational function integral necessary and sufficient condition |
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