## #2712 laplace transform of integral bug

None
open
nobody
5
2015-01-17
2014-03-29
No
```/* [wxMaxima: title   start ]
Laplace Transform of integral (in source domain) bugs
[wxMaxima: title   end   ] */
/* [wxMaxima: comment start ]
wxMaxima 13.04.2 Windows platform
[wxMaxima: comment end   ] */
/* [wxMaxima: input   start ] */
declare(C,constant)\$
/* [wxMaxima: input   end   ] */
/* [wxMaxima: input   start ] */
display_format_internal : true\$
noundisp : true\$
/* [wxMaxima: input   end   ] */
/* [wxMaxima: comment start ]
Laplace Transform of Constant times Integral of X(t)dt should be C/s times LT(X(t)):
C/s * 'laplace(X(t),t,s)
[wxMaxima: comment end   ] */
/* [wxMaxima: input   start ] */
(assume(s>0), lti1: laplace((C*integrate(X(t),t)),t,s));
/* [wxMaxima: input   end   ] */
/* [wxMaxima: comment start ]
Laplace Transform of 1/C times Integral of X(t)dt should be 1/Cs times LT(X(t)):
1/(C*s) * 'laplace(X(t),t,s)
[wxMaxima: comment end   ] */
/* [wxMaxima: input   start ] */
(assume(s>0), lti1: laplace((1/C*integrate(X(t),t)),t,s));
/* [wxMaxima: input   end   ] */
/* [wxMaxima: comment start ]
Constants, C or 1/C should be pulled out in front of LT.
Ok. integral needs to be one-sided definite instead.
[wxMaxima: comment end   ] */
/* [wxMaxima: input   start ] */
(assume(s>0), lti2: laplace((C*integrate(X(t),t,0,inf)),t,s));
/* [wxMaxima: input   end   ] */
/* [wxMaxima: comment start ]
Result should be: C/s * 'laplace(X(t),t,s), not C/s * one-sided integral of X(t)dt...
Try specint next:
[wxMaxima: comment end   ] */
/* [wxMaxima: input   start ] */
(assume(s>0), lti3: specint(C *'integrate(X(t)*exp(-s*t),t,0,inf),t));
/* [wxMaxima: input   end   ] */
/* [wxMaxima: comment start ]
Again, constant C should be pulled out in front. Result should be C/s * LT(X(t))...
[wxMaxima: comment end   ] */
/* [wxMaxima: comment start ]
Now, substitute correct result for lti2. Manual fix is possible:
[wxMaxima: comment end   ] */
/* [wxMaxima: input   start ] */
lti2: subst('laplace(X(t),t,s),integrate(X(t),t,0,inf),lti2);
/* [wxMaxima: input   end   ] */
```
1 Attachments

## Discussion

• Robert Dodier - 2014-07-04
• Description has changed:

Diff:

```--- old
+++ new
@@ -1,3 +1,4 @@
+~~~~
/* [wxMaxima: title   start ]
Laplace Transform of integral (in source domain) bugs
[wxMaxima: title   end   ] */
@@ -48,3 +49,4 @@
/* [wxMaxima: input   start ] */
lti2: subst('laplace(X(t),t,s),integrate(X(t),t,0,inf),lti2);
/* [wxMaxima: input   end   ] */
+~~~~
```

• Robert Dodier - 2014-07-04

Enclosing input file content in 4 tildes to show it is code.

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