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Hi,

Here an example of integral that Maple 17 cannot calculate (mean of standard Gumbel distribution)

> G:=int(x*exp(-x)*exp(-exp(-x)), x = -infinity .. infinity);

The result is known as the Euler-Mascheroni constant as shown by a numerical computation:

 > evalf(G);

0.5772156649

>  identify(%, extension = [gamma]);

gamma

> evalf(gamma)

0.5772156649

Also, it cannot compute the variance

>  V:=int((x-gamma)^2*exp(-x)*exp(-exp(-x)), x = -infinity .. infinity);

Numerical result gives

> evalf(V)

1.644934067

> identify(%)

Pi^2/6

which is the exact result. However, Maple 17 can compute the exact median value

> solve(int(f(x), x = -infinity .. alpha) = 1/2, alpha);

-ln(ln(2)

which is the right result.
integral

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