在积分求值过程中,对于象integral from n=0 to π ln(sinθ)dθ,integral from n=0 to π ln(x+1/x)dx/(1+x~2),integral from n=0 to 2π sin~nx/(sin~nx+cos~nx)dx等类型的积分,使用一般的常规解法将是十分麻烦的,有的甚至是不可能求解的。然而,使用一种特殊的解法——用定积分的性质去寻求上述各类积分值的求法,却可以取到意想不到的效果。 为解决上述问题,我们首先给出几个积分性质——这些 In the integral evaluation process, for an integral integral of n = 0 to π ln (sin θ) dθ, integral from n = 0 to π ln (x + 1 / x) dx / (1 + x ~ 2) = 0 to 2π sin ~ nx / (sin ~ nx + cos ~ nx) dx and other types of integration, the use of general conventional solution will be very troublesome, and some can not even be solved. However, the use of a special solution - the nature of the definite integral to seek these kinds of integral values ​​- can yield unexpected results. To solve the above problem, let us first give some integral nature - these