Ldefint is strictly less powerful than defint, or
should be. By ignoring singularities in the range
of integration it can get wrong answers. Defint is
not supposed to get wrong answers. The commercial
macsyma has a flag to forego the analysis needed for
definite integration, which is probably a better way
to go. ldefint is a 2 line program that calls indefinite
integration and does 2 substitutions.
RJF
Felix E. Klee wrote:
> Hi,
>
> take a look at this:
> (C133) integrand:1/(sqrt(2)+sin(x));
> (D133) 1/(SIN(x)+SQRT(2))
> (C134) integrate(integrand,x,0,2*%pi);
> (D134) 2*%PI
> (C135) defint(integrand,x,0,2*%pi);
> (D135) 2*%PI
> (C136) ldefint(integrand,x,0,2*%pi);
> (D136) 0
>
> Now, I have some questions:
> 1. Judging from the info pages I assumed that "ldefint" is more powerful
> than "defint". Then why does it return the wrong result but "integrate"
> and "defint" return the correct result?
> 2. Maxima returns a non continuous indefinite integral:
> (C214) ratsimp(integrate(integrand,x));
> (D214) 2*ATAN((SQRT(2)*SIN(x)+COS(x)+1)/(COS(x)+1))
> Shouldn't integrate always return a continuous function when the
> integrand is continuous?
> 3. Why are there both "integrate" and "defint"? According to the
> documentation they are the same. Shouldn't "defint" be flagged as
> deprecated?
>
> Felix
>
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