maple_10.mw

> restart;
 

> trace(int);
 

> infolevel[all]:=2;
 

> printlevel:= 20;
 

> int(x^3*exp(arcsin(x))/sqrt(1-x^2),x);
 

>
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[int:-ModuleApply]
2
20
{--> enter arcsin, args = x
{--> enter type/SymbolicInfinity, args = x
false
<-- exit type/SymbolicInfinity (now in arcsin) = false}
{--> enter arcsin/normal, args = x
{--> enter tools/csgn_k_times_k, args = x, x
false
false
<-- exit tools/csgn_k_times_k (now in arcsin/normal) = false}
1
x
{--> enter tools/sign, args = x
`+`(`-`(x))
1
<-- exit tools/sign (now in arcsin/normal) = 1}
1
table( [( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`(6, `/`(1, 2)), `*`(`+`(1, `-`(`*`(`/`(1, 3), `*`(`^`(3, `/`(1, 2))))))))))) ) = `+`(`*`(`/`(1, 12), `*`(Pi))), ( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`...
table( [( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`(6, `/`(1, 2)), `*`(`+`(1, `-`(`*`(`/`(1, 3), `*`(`^`(3, `/`(1, 2))))))))))) ) = `+`(`*`(`/`(1, 12), `*`(Pi))), ( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`...
table( [( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`(6, `/`(1, 2)), `*`(`+`(1, `-`(`*`(`/`(1, 3), `*`(`^`(3, `/`(1, 2))))))))))) ) = `+`(`*`(`/`(1, 12), `*`(Pi))), ( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`...
arcsin(x)
`+`(`-`(arcsin(x)))
arcsin(x)
<-- exit arcsin/normal (now in arcsin) = arcsin(x)}
arcsin(x)
arcsin(x)
<-- exit arcsin (now at top level) = arcsin(x)}
{--> enter exp, args = arcsin(x)
{--> enter type/SymbolicInfinity, args = arcsin(x)
false
<-- exit type/SymbolicInfinity (now in exp) = false}
value remembered (in exp): type/SymbolicInfinity(arcsin(x)) -> false
arcsin
x
exp(arcsin(x))
exp(arcsin(x))
<-- exit exp (now at top level) = exp(arcsin(x))}
{--> enter sqrt:-ModuleApply, args = -x^2+1
`+`(`-`(`*`(`^`(x, 2))), 1)
1
-1
`+`(`*`(`^`(x, 2)), `-`(1))
{--> enter sqrt:-ModuleApply, args = 1
1
<-- exit sqrt:-ModuleApply (now in sqrt:-ModuleApply) = 1}
1
-1
1
{--> enter psqrt, args = x^2-1
{--> enter psqrt/psqrt, args = x^2-1
`+`(`*`(`^`(x, 2)), `-`(1))
1
{x}
1
[2]
1
<-- ERROR in psqrt/psqrt (now in psqrt) = _NOSQRT}
_NOSQRT
_NOSQRT
<-- exit psqrt (now in sqrt:-ModuleApply) = _NOSQRT}
_NOSQRT
`*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))
<-- exit sqrt:-ModuleApply (now at top level) = (-x^2+1)^(1/2)}
{--> enter int:-ModuleApply, args = x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x
{--> enter type/satisfies, args = exp(arcsin(x)), proc (f) options operator, arrow; (op(0, f))::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(%, f0, 1 .. 1) = 1 end proc)), And(indexed, satisfies(proc (f0) options operator, arrow; (subsop(0 = op(0, f0), f))::'inertfunction' end proc)))) end proc
proc (f) options operator, arrow; (op(0, f))::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
proc (f) options operator, arrow; (op(0, f))::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
{--> enter unknown, args = exp(arcsin(x))
exp::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
<-- exit unknown (now in type/satisfies) = exp::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(%, f0, 1 .. 1) = 1 end proc)), And(indexed, satisfies(proc (f0) options operator, arrow; (subsop(0 = op(0, f0), exp(arcsin(x))))::'inertfunction' end proc))))}
exp::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
exp::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
false
<-- exit type/satisfies (now in int:-ModuleApply) = false}
{--> enter type/satisfies, args = arcsin(x), proc (f) options operator, arrow; (op(0, f))::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(%, f0, 1 .. 1) = 1 end proc)), And(indexed, satisfies(proc (f0) options operator, arrow; (subsop(0 = op(0, f0), f))::'inertfunction' end proc)))) end proc
proc (f) options operator, arrow; (op(0, f))::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
proc (f) options operator, arrow; (op(0, f))::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
{--> enter unknown, args = arcsin(x)
arcsin::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
<-- exit unknown (now in type/satisfies) = arcsin::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(%, f0, 1 .. 1) = 1 end proc)), And(indexed, satisfies(proc (f0) options operator, arrow; (subsop(0 = op(0, f0), arcsin(x)))::'inertfunction' end proc))))}
arcsin::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
arcsin::(Or(And(symbol, satisfies(proc (f0) options operator, arrow; SearchText(
false
<-- exit type/satisfies (now in int:-ModuleApply) = false}
{--> enter Main, args = x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x
{--> enter Initialize, args =
<-- exit Initialize (now in Main) = }
{--> enter EnvToOptions, args = [x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x], [CauchyPrincipalValue = false, formula = true]
{formula = true, CauchyPrincipalValue = false}
[`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x]
[`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x]
[`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x]
CauchyPrincipalValue
AllSolutions
Continuous
{formula = true, CauchyPrincipalValue = false}
<-- exit EnvToOptions (now in Main) = formula = true, CauchyPrincipalValue = false}
{--> enter Exact, args = x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x, Main, formula = true, CauchyPrincipalValue = false
{CauchyPrincipalValue = false}
CauchyPrincipalValue
false
AllSolutions
Continuous
[`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x], []
`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2))))
x
{}
false
gcd/LinZip: Using 8-byte integer mod
gcd/LinZip: Using 8-byte integer mod
int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/indef2: trying integration by parts
simplify/do: applying simplify/exp function to expression
combine: combining with respect to exp
int/rischnorm: enter Risch-Norman integrator
radfield: computing a basis for  {}
radfield: over  {}
radfield: options are {}
radfield: field is {}
radfield: extension degree is 1
radfield: computing a basis for  {}
radfield: over  {}
radfield: options are {}
radfield: field is {}
radfield: extension degree is 1
int/rischnorm: exit Risch-Norman integrator
int/risch: enter Risch integration
radfield: computing a basis for  {I}
radfield: over  {}
radfield: options are {}
radnormal/addtop: adding 1 algebraics
radnormal/addtop: over  {}
radnormal/addrads: adding 1 radicals
radnormal/addrads: over  {}
radnormal/addone: adding a single radical
radfield: field is {RootOf(_Z^2+1 index = 1)}
radfield: extension degree is 2
radfield: computing a basis for  {I}
radfield: over  {}
radfield: options are {}
radfield: field is {RootOf(_Z^2+1 index = 1)}
radfield: extension degree is 2
simplify/do: applying simplify/radical function to expression
simplify/do: applying simplify/sqrt function to expression
sqrfree/Yun: square-free factorization in x
sqrfree/Yun: square-free factorization in x
sqrfree/Yun: square-free factorization in x
simplify/do: applying simplify/power function to expression
simplify/do: applying simplify/power function to expression
int(`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x)
int(`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x)
<-- exit Exact (now in Main) = int(x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x)}
<-- exit Main (now in int:-ModuleApply) = int(x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x)}
<-- exit int:-ModuleApply (now at top level) = int(x^3*exp(arcsin(x))/(-x^2+1)^(1/2), x)}
int(`/`(`*`(`^`(x, 3), `*`(exp(arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x) (1)
 

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