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# Edit detail for Symbolic Integration revision 2 of 12

 1 2 3 4 5 6 7 8 9 10 11 12 Editor: mcd Time: 2009/06/26 00:20:27 GMT-7 Note: solvin

```added:

From mcd Fri Jun 26 00:20:27 -0700 2009
From: mcd
Date: Fri, 26 Jun 2009 00:20:27 -0700
Subject: solvin
Message-ID: <20090626002027-0700@axiom-wiki.newsynthesis.org>

int(sqrt(x), x);
```

## Errors in symbolic integration

AXIOM Examples

1)

axiom
```integrate(sin(x)+sqrt(1-x^3),x)
>> Error detected within library code:
failed - cannot handle that integrand```

 `int(sin(x)+sqrt(1-x^3),x);` reduce

2)

axiom
```integrate(sqrt(1-log(sin(x)^2)),x)
>> Error detected within library code:
integrate: implementation incomplete (constant residues)```

 `int(sqrt(1-log(sin(x)^2)),x);` reduce

3)

axiom
```integrate(sqrt(sin(1/x)),x)
>> Error detected within library code:
integrate: implementation incomplete (constant residues)```

That seems strange given the claims about the "completeness" of Axiom's integration algorithm! But to be fair, Maple also returns this integral unevaluated.

 `int(sqrt(sin(1/x)),x);` reduce

4)

axiom
`integrate(sqrt(sin(x)),x)`
 (1)
Type: Union(Expression Integer,...)

 `int(sqrt(sin(x)),x);` reduce

For this Maple 9 gives the following result:

 (2)

And Mathematica 4 gives:

 (3)

symbolic integration
Tue, 22 Mar 2005 11:48:00 -0600 reply
axiom
`integrate(exp(-x^2),x)`
 (4)
Type: Union(Expression Integer,...)
Errorfunction
Wed, 23 Mar 2005 08:23:21 -0600 reply
axiom
`integrate(exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)`
 (5)
Type: Union(f1: OrderedCompletion? Expression Integer,...)

axiom
```int(x,x)
There are no exposed library operations named int but there are 5
unexposed operations with that name. Use HyperDoc Browse or issue
)display op int
Cannot find a definition or applicable library operation named int
with argument type(s)
Variable x
Variable x
Perhaps you should use "@" to indicate the required return type,
or "\$" to specify which version of the function you need.```

axiom
`integrate(x,x)`
 (6)
Type: Polynomial Fraction Integer

axiom
```axiomintegrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
There are no library operations named axiomintegrate
Use HyperDoc Browse or issue
)what op axiomintegrate
to learn if there is any operation containing " axiomintegrate "
in its name.
Cannot find a definition or applicable library operation named
axiomintegrate with argument type(s)
Expression Integer
SegmentBinding OrderedCompletion Integer
Perhaps you should use "@" to indicate the required return type,
or "\$" to specify which version of the function you need.```

axiom
`integrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)`
 (7)
Type: Union(fail: failed,...)

The answer should be:

 (8)

integrate(exp(x)/x^2) --unknown, Thu, 25 Aug 2005 05:57:53 -0500 reply
Axiom does not perform the integration (while it perform the integration of exp(x)/x ), but the integration can be given in terms of Ei(x)

integrate(exp(x)/x^2,x) --> Ei(x)-exp(x)/x

int(sqrt(x), x)

int(sqrt(x), x);