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## Re: [Axiom-developer] axiom integrate() return wrong result

**From**: |
daly |

**Subject**: |
Re: [Axiom-developer] axiom integrate() return wrong result |

**Date**: |
Sat, 29 Nov 2014 06:54:43 -0600 |

Thank you for taking the time to generate a bug report.
>*I'm exploring the power of integrate() in Axiom, and find that*
>
>*f:=1/(sin(x)^4+1)*
>*a:=integrate(f,x)*
>*b:=differentiate(a,x,1)*
>*draw(b, x=0..4)*
>*draw(f, x=0..4)*
>
>*give me inconsistent result.*
Yes, Axiom did give an "inconsistent result", which is most likely
a "wrong" result as well.
>*If change to say f:=1/(x^4+1), then I get consistent result.*
Actually that looks wrong also. Click on the graph to bring up
the control panel, click on "units on", and you'll find that
the curves are different. The integrate/differentiate is failing.
>*Also tested latest code (2014-11-28) in github(git clone *
>*git://github.com/daly/axiom.git).*
>
>*bug 7251, 7147, 7085/15, 7084/293 may be related to this bug?*
>*Note that strictly speaking, integrate(1/(x^4+1),x) also returns an *
>*incorrect result (correct only when understand it as a complex *
>*multi-value function).*
I don't know if these are related (the integration code is not
simple and chasing bugs is time-consuming).
>*One more note: I have tried FriCAS (also the latest version), it give me *
>*the correct integration result.*
I tried FriCAS (2013-04-06 on MAC OS X).
I found that
f:=1/(sin(x)^4+1)
a:=integrate(f,x)
b:=differentiate(a,x,1)
draw(b, x=0..4)
fails with the message:
draw(b,x=0..4)
Compiling function %O with type DoubleFloat -> DoubleFloat
>> System error:
Too large to be represented as a SINGLE-FLOAT
14353327979561593211089438493917727500805625855126443
Also, the graphs show that the result is wrong when you turn
"units on".
When I get near my office I will try the test in Maple and MMA.
Thanks for the bug report.
Can you send your full name to "address@hidden" so I
can list you in the credits?
Tim

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**Re: [Axiom-developer] axiom integrate() return wrong result**,
*daly* **<=**