找不到明确的积分 [英] Explicit integral could not be found

问题描述

如果我尝试评估以下积分，我将收到一个众所周知的错误:找不到明确的积分"

I am getting a well-known error of "Explicit integral could not be found" if I try to evaluate following integral

syms z;
funz=1./(1+exp((z*z-0.5)/0.1));
Integ2=int(funz,z,0,inf)

我得到警告:

Warning: Explicit integral could not be found.        
Integ2 =   
int(1/(exp(10*z^2 - 5) + 1), z == 0..Inf)

Mathematica将该积分评估为0.693.

Mathematica evaluates this integral to 0.693.

我尝试将积分下限替换为较小的有限数字(0.001)，但这无济于事. 请帮助确定解决此问题的方法. 任何帮助表示赞赏. 非常感谢！

I have tried replacing lower integration limit to some small finite number (0.001) but that doesn't help. Please help in identifying the fix for this problem. Any help is appreciated. Thanks a lot !

推荐答案

尝试可变精度算术，vpa:

syms z; 
funz=1./(1+exp((z*z-0.5)/0.1));

Integ2=int(funz,z,0,inf)
Warning: Explicit integral could not be found. 

Integ2 =
int(1/(exp(10*z^2 - 5) + 1), z = 0..Inf)

vpa(Integ2,5)  % 5 is the number of significant digits
ans =     
0.69305

请参见文档近似定积分"中的最后一个示例. 引用:

See the last example in the documentation, "Approximate Definite Integrals". Quote:

如果int无法计算定积分的闭合形式，请尝试 使用vpa在数值上近似该积分.

If int cannot compute a closed form of a definite integral, try approximating that integral numerically using vpa.

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