> | restart; |
> | trace(int); |
> | infolevel[all]:=2; |
> | printlevel:= 20; |
> | int(x^3*exp(arcsin(x))/sqrt(1-x^2),x); |
> |
{--> enter arcsin, args = x
{--> enter type/SymbolicInfinity, args = x |
|
<-- exit type/SymbolicInfinity (now in arcsin) = false}
{--> enter arcsin/normal, args = x {--> enter tools/csgn_k_times_k, args = x, x |
|
<-- exit tools/csgn_k_times_k (now in arcsin/normal) = false} | |
{--> enter tools/sign, args = x | |
<-- exit tools/sign (now in arcsin/normal) = 1} | |
<-- exit arcsin/normal (now in arcsin) = arcsin(x)} | |
<-- exit arcsin (now at top level) = arcsin(x)}
{--> enter exp, args = arcsin(x) {--> enter type/SymbolicInfinity, args = arcsin(x) |
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<-- exit type/SymbolicInfinity (now in exp) = false}
value remembered (in exp): type/SymbolicInfinity(arcsin(x)) -> false |
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<-- exit exp (now at top level) = exp(arcsin(x))}
{--> enter sqrt:-ModuleApply, args = -x^2+1 |
|
{--> enter sqrt:-ModuleApply, args = 1 | |
<-- exit sqrt:-ModuleApply (now in sqrt:-ModuleApply) = 1} | |
{--> enter psqrt, args = x^2-1
{--> enter psqrt/psqrt, args = x^2-1 |
|
<-- ERROR in psqrt/psqrt (now in psqrt) = _NOSQRT} | |
<-- exit psqrt (now in sqrt:-ModuleApply) = _NOSQRT} | |
<-- 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 |
|
{--> enter unknown, args = exp(arcsin(x)) | |
<-- 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))))} | |
<-- 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 |
|
{--> enter unknown, args = arcsin(x) | |
<-- 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))))} | |
<-- 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] |
|
<-- 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 |
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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 |
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sqrfree/Yun: square-free factorization in x
sqrfree/Yun: square-free factorization in x |
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simplify/do: applying simplify/power function to expression
simplify/do: applying simplify/power function to expression |
|
<-- 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)} |
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(1) |
> |