1 | initial version |

This is a bug. Furthermore, it is *not* a `maxima`

bug, as it is often the case. Here, Sage truly screws things up itself :

Maxima doesn't give a false answer :

sage: maxima.integrate(sqrt(1+cos(x)^2),x).sage()

integrate(sqrt(cos(x)^2 + 1), x)

When one tries to "ease" the problem,

maxima doesn't recognize the "obvious", but does not give a false answer :

sage: maxima.integrate(sqrt(1-m*sin(x)^2),x).sage()

integrate(sqrt(-m*sin(x)^2 + 1), x)

Sage does :

sage: integrate(sqrt(1-m

*sin(x)^2),x) 1/4*m*x - 1/8*m*sin(2*x)

BTW : what is expected :

```
sage: elliptic_e(x,1/2).diff(x)
sqrt(-1/2*sin(x)^2 + 1)
```

One can easily check that `sympy`

, `giac`

and `fricas`

all fail to integrate, but that none of them gives misleading "answers".

This one does not seem to be related to existing indefinite integral bugs, and is an original, genuine, Sage-specific one. Reported as Trac#26563

2 | No.2 Revision |

This is a bug. Furthermore, it is *not* a `maxima`

bug, as it is often the ~~case. ~~case.
Here, Sage truly screws things up ~~itself :~~itself:

Maxima doesn't give a false

~~answer :~~sage: maxima.integrate(sqrt(1+cos(x)^2),x).sage()

answer:

`sage: maxima.integrate(sqrt(1+cos(x)^2),x).sage() integrate(sqrt(cos(x)^2 + 1),`

~~x)~~x)When one tries to "ease" the problem,

maxima doesn't recognize the "obvious", but does not give a false

~~answer :~~sage: maxima.integrate(sqrt(1-m*sin(x)^2),x).sage()

answer:

`sage: maxima.integrate(sqrt(1-m*sin(x)^2),x).sage() integrate(sqrt(-m*sin(x)^2 + 1),`

~~x)~~x)Sage

~~does :~~sage: integrate(sqrt(1-m

*sin(x)^2),x) 1/4*m*x does:*`sage: integrate(sqrt(1-m*sin(x)^2),x) 1/4*m*x -`

~~1/8~~`m`

*sin(2*x)1/8*m*sin(2*x)

~~BTW : ~~BTW: what is ~~expected :~~expected:

```
sage: elliptic_e(x,1/2).diff(x)
sqrt(-1/2*sin(x)^2 + 1)
```

One can easily check that `sympy`

, `giac`

and `fricas`

all fail to ~~integrate, ~~integrate,
but that none of them gives misleading "answers".

This one does not seem to be related to existing indefinite integral ~~bugs, ~~bugs,
and is an original, genuine, Sage-specific one. Reported ~~as Trac#~~as
~~26563~~Trac #26563~~ ~~

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