Opened 7 years ago

# unsolved piecewise integrals metaticket

Reported by: Owned by: rws major sage-wishlist calculus integration kcrisman N/A

Archive of removed doctests testing the `abs_integrate` Maxima package (removed with #12731).

```sage: y = function('y')
sage: integrate(1/sqrt(abs(y(x))), y(x))  # ok
integrate(diff(y(x), x)/sqrt(abs(y(x))), x)
```
```sage: integrate(sgn(x) - sgn(1-x), x)   # ok
abs(x - 1) + abs(x)
```
```sage: integrate(1 / (1 + abs(x-5)), x, -5, 6)     # ok
log(11) + log(2)
```
```sage: integrate(1/(1 + abs(x)), x)   # ok
log(abs(x*sgn(x) + 1))/sgn(x)
```
```sage: integrate(cos(x + abs(x)), x)      # ok
sin(x*sgn(x) + x)/(sgn(x) + 1)
```
```sage: integrate(sqrt(x + sqrt(x)), x).canonicalize_radical()      # ok
1/12*(8*x + 2*sqrt(x) - 3)*sqrt(x + sqrt(x)) - 1/8*log(abs(2*sqrt(x + sqrt(x)) - 2*sqrt(x) - 1))
```
```sage: integrate(abs(x^2 - 1), x, -2, 2) # ok
4
```
```sage: f = sqrt(x + 1/x^2)
sage: integral(f, x)  # to be checked
2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(sqrt(x^3 + 1) - 1)
```
```sage: f1(x) = e^(-abs(x))
sage: f = Piecewise([[(-infinity, infinity), f1]])
sage: f.integral(definite=True)  # ok
2
sage: f.integral()
Piecewise defined function with 1 parts, [[(-Infinity, +Infinity), x |--> -1/2*((sgn(x) - 1)*e^(2*x) - 2*e^x*sgn(x) + sgn(x) + 1)*e^(-x) - 1]]
```

Also, these have their own tickets:

• `integrate(x * sgn(x^2 - 1/4), x, -1, 0)` (#11590)
• `integral(log(abs(2*sin(u))), u, 0, pi/3)` (#17468)
• `integrate(abs(cos(x)),x,0,pi)` (#17511)

### comment:1 Changed 7 years ago by rws

• Description modified (diff)
• Milestone changed from sage-6.6 to sage-wishlist

### comment:3 Changed 7 years ago by rws

• Description modified (diff)

### comment:4 Changed 7 years ago by jdemeyer

Never remove doctests, mark them as `# known bug`.

### comment:6 Changed 3 years ago by chapoton

EDIT: 6 out of the first seven are working after #27958 (and none without)

Last edited 3 years ago by chapoton (previous) (diff)

### comment:7 Changed 3 years ago by chapoton

This one hangs in giac:

```integrate(sqrt(x + sqrt(x)), x)
```

### comment:8 Changed 3 years ago by chapoton

• Description modified (diff)

### comment:9 Changed 9 months ago by chapoton

• Description modified (diff)

### comment:10 Changed 9 months ago by chapoton

• Keywords integration added; abs_integrate removed
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