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## #2788 says integral is divergent when it clearly is not

None
open
nobody
None
5
2014-10-23
2014-07-24
dan hayes
No

Claims integral divergent when it is obviously convergent and well defined.

wxMaxima version: 13.4.0
Maxima version: 5.31.1
Maxima build date: 2013-09-24 09:49:12
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

```(assume(a>0),integrate(integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),r,0,inf))
```

says integral is divergent and obviously it is NOT. Upper limit is obviously 0

```(t:integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),ratsimp(subst(r=0,integrate(t,r))))
```

gives

```-4*a/(k^4+2*a^2*k^2+a^4)
```

## Discussion

• Robert Dodier
2014-07-29

• Description has changed:

Diff:

```--- old
+++ new
@@ -7,9 +7,18 @@
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

+~~~~
(assume(a>0),integrate(integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),r,0,inf))
+~~~~

says integral is divergent and obviously it is NOT. Upper limit is obviously 0

+~~~~
(t:integrate(exp(-a*r+%i*k*r*w)*r^2,w,-1,1),ratsimp(subst(r=0,integrate(t,r))))
-gives -4*a/(k^4+2*a^2*k^2+a^4)
+~~~~
+
+gives
+
+~~~~
+-4*a/(k^4+2*a^2*k^2+a^4)
+~~~~
```