凑微分法、换元法 英文

凑微分法、换元法英文
Integration by parts is called "integral differentiation" in Chinese.
Substitution method is called "change of variable" in Chinese.
1. The integral of a product of two functions can be evaluated using the integration by parts method.
利用凑微分法，可以求解一个函数乘积的积分。

2. The substitution method involves substituting a new variable to simplify the integral.
换元法涉及将新的变量代入以简化积分。

3. In the integration by parts method, the product of two functions is split into two differentials.
在凑微分法中，两个函数的乘积被拆分成两个微分。

4. The substitution method makes the integral easier to handle by replacing the variable with a new one.
换元法通过用新的变量代替原来的变量，使积分更容易处理。

5. To use the integration by parts method, one function is chosen to differentiate and the other to integrate.
使用凑微分法，选择一个函数进行微分，另一个函数进行积分。

6. The substitution method is particularly useful when dealing with integrals involving trigonometric functions.
换元法在处理涉及三角函数的积分时特别有用。

7. Integration by parts is often used to evaluate integrals involving exponential functions.
凑微分法常用于求解涉及指数函数的积分。

8. The substitution method allows us to express an integral in terms of a different variable, making it easier to solve.
换元法使我们能够用不同的变量表达积分，从而更容易求解。

9. In the integration by parts method, the goal is to simplify the integral by differentiating and integrating different terms.
在凑微分法中，目标是通过对不同项进行微分和积分来简化积分。

10. The substitution method involves finding a new expression for the original variable in terms of the new variable.
换元法涉及找到用新的变量表示原来变量的新表达式。

11. Integration by parts is a powerful technique for evaluating a wide range of integrals.
凑微分法是一种用于求解各种积分的强大技巧。

12. By using the substitution method, we can transform a complicated integral into a simpler form.
通过使用换元法，我们可以将复杂的积分转化为简单的形式。

13. The integration by parts method can be used in situations where direct integration is not possible.
凑微分法可以应用于直接积分不可行的情况。

14. The substitution method is based on the chain rule of differentiation.
换元法基于微分的链式法则。

15. To get the best result, careful consideration should be given when choosing functions for the integration by parts method.
为了获得最佳结果，在选择凑微分法的函数时应谨慎考虑。

16. The substitution method is often used to simplify integrals involving square root functions.
换元法通常用于简化涉及平方根函数的积分。

17. The integration by parts method is based on the product rule of differentiation.
凑微分法基于微分的乘积法则。

18. The substitution method allows us to change the variable of integration and manipulate the integral accordingly.
换元法可以改变积分的变量，并相应地操作积分。

19. The integration by parts method can be used to solve definite integrals as well as indefinite integrals.
凑微分法可以用于求解定积分和不定积分。

20. The substitution method is often used in calculus courses to teach students how to simplify integrals.
换元法经常在微积分课程中用于教授学生如何简化积分。

21. Integration by parts and substitution are two commonly used techniques in calculus.
凑微分法和换元法是微积分中常用的两种技巧。

22. The substitution method is especially useful for evaluating integrals involving rational functions.
换元法对于求解涉及有理函数的积分特别有用。

23. In the integration by parts method, the choice of which function to differentiate and which function to integrate is crucial.
在凑微分法中，选择哪个函数进行微分，哪个函数进行积分是关键。

24. The substitution method allows us to transform a complicated integral into a standard form that can be easily solved.
换元法使我们能够将复杂的积分转化为标准形式，从而可以轻松求解。

25. Integration by parts and substitution are powerful tools that can simplify complex integrals and solve various mathematical problems.
凑微分法和换元法是强大的工具，可以简化复杂的积分并解决各种数学问题。