Opened 6 years ago

# unsolved piecewise integrals metaticket

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

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

```integrate(1/sqrt(abs(y(x))), y(x))
integrate(sgn(x) - sgn(1-x), x)
integrate(1 / (1 + abs(x-5)), x, -5, 6)
integrate(1/(1 + abs(x)), x)
integrate(cos(x + abs(x)), x)
integrate(abs(x^2 - 1), x, -2, 2)

sage: f = sqrt(x + 1/x^2)
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)
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 6 years ago by rws

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

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

• Description modified (diff)

### comment:4 Changed 6 years ago by jdemeyer

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

### comment:6 Changed 2 years ago by chapoton

EDIT: 6 out of the first seven are working after #27958

Version 2, edited 2 years ago by chapoton (previous) (next) (diff)

### comment:7 Changed 2 years ago by chapoton

This one hangs in giac:

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

### comment:8 Changed 23 months ago by chapoton

• Description modified (diff)
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