例如，在微积分课程中，记下分步积分法的公式并不是特别难。
For example, in a calculus course it's not terribly difficult to memorize the formula for integration by parts for integrals.
第二换元积分法是求函数不定积分的一种重要方法，具有一定的适用范围，对某些无理函数的积分的求解通常使用该方法。
The integration by second substitution is an important method of calculating indefinite integral, it has a certain application, it usually applies to calculate some integrals of irrational function.
本文给出了用定积分的分部积分法求解二重积分的一种方法。
This paper gives a method to solve double integration by integral subsection integration.
其次，将逐项积分结果求和并证明了求和结果与传统直接积分法的塑性功率表达式相同；
Then, sum of the termwise integrated results is proved to be equal to that obtained from traditional immediate integration for plastic deformation power.
奇异积分问题是边界元法最大的问题之一，本文采用高斯积分法来解决。
Singularity integral is one of the most serious problems in FEM, and this paper adopts gauss integral to deal with it.
文中给出一个算例，其数值结果与直接积分法、精细积分法作了比较，文中方法对结构动力响应计算是十分有效的。
A numerical example is given, the results are compared with direct integration method and precision integration method. It is quite effective for computing the structural dynamic response.
分析了不定积分的四种基本求解方法：直接积分、第一换元法、第二换元法、分部积分法。
There are four solutions of indefinite integration in paper: direct integration, the first exchangeable integration, the second exchange - able integration, parcel integration.
将小波配置方法和精细积分方法相结合，提出了一种对水土侵蚀模型进行数值分析的新方法——小波精细积分法。
A new numerical method on rill erosion model was proposed by combining the wavelet collocation method with the precise integration method, which is called wavelet precise integration method (WPIM).
在精细时程积分法的基础上，将精细积分法与振型叠加法结合起来，提出振型分解精细积分法。
This new method is called the mode decomposition precise integration method because it is the result of the combination of the mode decomposition method with the precise integration method.
讨论了精细直接积分法中积分方法选择问题。
The selection of numerical integration method of precise direct integration is discussed in this paper.
利用单点子域积分法推出了求解梁结构动位移响应的积分格式。
The single point integration scheme of dynamic displacement of beam structure is reckoned by using single point subdomain precise integration in the paper.
采用精细时程积分法及状态方程直接积分法，讨论了求解动力响应问题的时程积分方式。
By means of the precise time-integration method and the method of direct integration of state equation, the mode of the time-integration has been discussed on the structural dynamical responses.
目前的数值积分方法包括显式积分法与隐式积分法两大类。
Currently, numerical integration methods are explicit method and implicit method.
传统的几何积分法、概率积分法解决不了的一些难题，用力学方法可能得到解决。
Some difficult problems which can not be solved by the conventional methods, such as geometric method and probability integration.
与减缩积分法不同，本方法采用多套函数去逼近单元的应变，而不涉及形成单刚时所采用的数值积分的阶次。
Unlike the reduced integration methods, the QCE technique USES multiple sets of functions to approximate strain and has no concern with the integration order.
通过计算机模拟和波面实际测量，对十字路径积分法、傅里叶变换积分法和区域波前重构法三种主要算法的重建精度进行了对比研究。
The simulation and the experiment results demonstrated the precision of cross path integration techniques, Fourier transform integration and area wave-front reconstruction method.
暨南大学张森文教授运用精细积分法的成果提出了状态方程直接积分法。
Professor Zhang Senwen from Jinan University created a new direct integration method which makes use of the precise integration method.
文中还根据积分中值定理证明了应用概率积分法求得的下沉等值线是椭圆形或圆形。
According to the theorem of integral mean value it is proved in this paper that by means of probability integral the subsidence equivalent curve is a circle or a ellipse.
本文讨论了积分法的一般原理，并推导了陀螺经纬仪定向积分测量法。
The general principle of the integral method is discussed in this paper. Then the oriented integral surveying method using gyro theodolite is derived.
高斯积分法是一个高精度的数值积分方法，它的计算结果精度胜过角柱体法与快速傅利叶法。
The Gaussian quadrature is a highly accurate numerical integrator and yields results that outperform those from the prism method and the FFT method.
高斯积分法是一个高精度的数值积分方法，它的计算结果精度胜过角柱体法与快速傅利叶法。
The Gaussian quadrature is a highly accurate numerical integrator and yields results that outperform those from the prism method and the FFT method.
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