#2385 integrate gives strange results

[drunas97]

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Maxima version: 5.26.0
Maxima build date: 22:48 1/15/2012
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
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I try to integrate functions of such a type:
Kvar(f,N,t1,t2):=N/(N-1)*(sin(%pi*f*t2)/(%pi*f*t2))^2*(1-(sin(N*%pi*f*t1)/(N*sin(%pi*f*t1)))^2)
they all are absolutely integrable.
but maxima gives:

integrate(Kvar(f,2,1,1),f,0,inf);
defint: integral is divergent.
-- an error. To debug this try: debugmode(true);

integrate(Kvar(f,2,1,1),f,0,inf),numer;
0.15915494309189*%pi

integrate(Kvar(f,2,1,1),f,0.0,inf),numer;
`quotient' by `zero'
-- an error. To debug this try: debugmode(true);

I thought the mistakes originate from defining Kvar(f,N,t1,t2) at f=0 (0/0), so i changed the integration limits:

integrate(Kvar(f,2,1,1),f,0.1,1);
-(2*%i*%pi*gamma_incomplete(-1,4*%i*%pi)-4*%i*%pi*gamma_incomplete(-1,2*%i*%pi)-2*%i*%pi*gamma_incomplete(-1,(2*%i*%pi)/5)+4*%i*%pi*gamma_incomplete(-1,(%i*%pi)/5)
-4*%i*%pi*gamma_incomplete(-1,-(%i*%pi)/5)+2*%i*%pi*gamma_incomplete(-1,-(2*%i*%pi)/5)+4*%i*%pi*gamma_incomplete(-1,-2*%i*%pi)-2*%i*%pi*gamma_incomplete(-1,-4*%i*%pi)-27
)/(4*%pi^2)

integrate(Kvar(f,2,1,1),f,0.1,1),numer;
`quotient' by `zero'
-- an error. To debug this try: debugmode(true);

At the same time:

quad_qag(Kvar(f,2,1,1),f,0.1,1,6);
[0.42152826647711,4.6799038697321796*10^-15,61,0]

[Dan Gildea]

seems to be fixed in current sources.

(%i13) Kvar(f,N,t1,t2):=N/(N-1)*(sin(%pi*f*t2)/(%pi*f*t2))^2*(1-(sin(N*%pi*f*t1)/(N*sin(%pi*f*t1)))^2);
(%o13) Kvar(f,N,t1,t2):=N/(N-1)*(sin(%pi*f*t2)/(%pi*f*t2))^2
*(1-(sin(N*%pi*f*t1)/(N*sin(%pi*f*t1)))^2)
(%i14) integrate(Kvar(f,2,1,1),f,0,inf);
(%o14) 1/2