This time XCAS and hp prime are really wrong! ! !

[yangyongkang]

Sorry, I am picking up XCAS or hp prime again. The first few times I wrote is the problem that hp prime or XCAS can't solve. This time I pointed out that hp prime or XCAS is really wrong. The prototype is to calculate int(abs(sin(x)/e^x), x, 0, +infinity). We know that the integrand removes the absolute value and becomes int(sin(x)/e^x,0, +infinity), using the Newton-Leibnitz formula is very good, XCAS gives an answer of 1/2, in fact the answer is correct, but after adding the absolute value, the XCAS answer is still given 1/2. Obviously wrong. We enter on Wolfram Mathematica 11.3

Code:

Integrate[Abs[Sin[x]/E^x], {x, 0, Infinity}]

I got the answer after running,

Code:

FullSimplify[%]

Code:

1/2 Coth[\[Pi]/2]

In addition, in fact, hp prime or XCAS can give int(e^(-x^2), x), and should also give int(sin(x)/e^(x^2), x) , but unfortunately, XCAS returned to the original