[Discussion] Solving the Limit Problem

[yangyongkang]

Several perverted integrals
(i)

Code:

evalf(int(1/(1+e^(1/x)),x,-1,1))

The answer is 1
xcas get

Code:

"Unidirectional limits are distincts 1,0 Error: Bad Argument Valu"

(ii)

Code:

int(x^2*tan(x)^2+x^2+2*x*tan(x)+1,x)

The answer is

Code:

x+x*tan(x)

(iii)

Code:

simplify(int((x*tan(x)+ln(x*cos(x))-1)/ln(x*cos(x))^2,x))

The answer is

Code:

x/ln(x*ln(x))