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Why won't thedoesn't Integrate command workevaluate an elliptic integral?

My code is

Integrate[1Integrate[ 1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, Infinity ∞}, 
           Assumptions -> 0 < d < c < b < a]

I know this is equal tocan be expressed be the completeincomplete elliptic integral of first kind (EllipticF), but the output isremains unevaluated

Integrate[1Integrate[ 1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, 
  a, \[Infinity] ∞}, 
           Assumptions -> 0 < d < c < b < a]

why is thatWhy does this happen? I am desperate

Why won't the Integrate command work?

My code is

Integrate[1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, Infinity}, 
 Assumptions -> 0 < d < c < b < a]

I know this is equal to the complete elliptic integral of first kind, but the output is

Integrate[1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, 
  a, \[Infinity]}, Assumptions -> 0 < d < c < b < a]

why is that? I am desperate

Why doesn't Integrate evaluate an elliptic integral?

My code is

Integrate[ 1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a,  ∞}, 
           Assumptions -> 0 < d < c < b < a]

I know this can be expressed be the incomplete elliptic integral of first kind (EllipticF), but the output remains unevaluated

Integrate[ 1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, a,  ∞}, 
           Assumptions -> 0 < d < c < b < a]

Why does this happen? I am desperate

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J. M.'s missing motivation ♦
J. M.'s missing motivation ♦
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My code is

Integrate[1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, Infinity}, 
 Assumptions -> 0 < d < c < b < a]

I know this is equal to the complete elliptic functionintegral of first kind, but the output is

Integrate[1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, 
  a, \[Infinity]}, Assumptions -> 0 < d < c < b < a]

why is that? I am desperate

My code is

Integrate[1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, Infinity}, 
 Assumptions -> 0 < d < c < b < a]

I know this is equal to the complete elliptic function of first kind, but the output is

Integrate[1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, 
  a, \[Infinity]}, Assumptions -> 0 < d < c < b < a]

why is that? I am desperate

My code is

Integrate[1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, Infinity}, 
 Assumptions -> 0 < d < c < b < a]

I know this is equal to the complete elliptic integral of first kind, but the output is

Integrate[1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, 
  a, \[Infinity]}, Assumptions -> 0 < d < c < b < a]

why is that? I am desperate

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Filippo Caleca
Filippo Caleca
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Why won't the Integrate command work?

My code is

Integrate[1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, Infinity}, 
 Assumptions -> 0 < d < c < b < a]

I know this is equal to the complete elliptic function of first kind, but the output is

Integrate[1/Sqrt[(-a + x) (-b + x) (-c + x) (-d + x)], {x, 
  a, \[Infinity]}, Assumptions -> 0 < d < c < b < a]

why is that? I am desperate