maple_10.mw

> restart;
trace(int);
infolevel[all]:=2;
printlevel:= 20;
int(x^3*exp(1)^arcsin(x)/sqrt(1-x^2),x);
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[int:-ModuleApply]
2
20
{--> enter exp, args = 1
exp(1)
exp(1)
<-- exit exp (now at top level) = exp(1)}
{--> 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), `*`(`^`(5, `/`(1, 2)))), `-`(`/`(1, 4)))) ) = `+`(`*`(`/`(1, 10), `*`(Pi))), ( permanent::(`+`(`*`(`/`(1, 2), `*`(`^`(2, `/`(1, 2)))))) ) = `+`(`*`(`/`(1, 4), ...
table( [( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`(5, `/`(1, 2)))), `-`(`/`(1, 4)))) ) = `+`(`*`(`/`(1, 10), `*`(Pi))), ( permanent::(`+`(`*`(`/`(1, 2), `*`(`^`(2, `/`(1, 2)))))) ) = `+`(`*`(`/`(1, 4), ...
table( [( permanent::(`+`(`*`(`/`(1, 4), `*`(`^`(5, `/`(1, 2)))), `-`(`/`(1, 4)))) ) = `+`(`*`(`/`(1, 10), `*`(Pi))), ( permanent::(`+`(`*`(`/`(1, 2), `*`(`^`(2, `/`(1, 2)))))) ) = `+`(`*`(`/`(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 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(1))^arcsin(x)/(-x^2+1)^(1/2), x
{--> enter type/satisfies, args = exp(1), 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(1)
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(1)))::'inertfunction' end proc))))}
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(1))^arcsin(x)/(-x^2+1)^(1/2), x
{--> enter Initialize, args =
<-- exit Initialize (now in Main) = }
{--> enter EnvToOptions, args = [x^3*(exp(1))^arcsin(x)/(-x^2+1)^(1/2), x], [CauchyPrincipalValue = false, formula = true]
{formula = true, CauchyPrincipalValue = false}
[`/`(`*`(`^`(x, 3), `*`(`^`(exp(1), arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x]
[`/`(`*`(`^`(x, 3), `*`(`^`(exp(1), arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x]
[`/`(`*`(`^`(x, 3), `*`(`^`(exp(1), 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(1))^arcsin(x)/(-x^2+1)^(1/2), x, Main, formula = true, CauchyPrincipalValue = false
{CauchyPrincipalValue = false}
CauchyPrincipalValue
false
AllSolutions
Continuous
[`/`(`*`(`^`(x, 3), `*`(`^`(exp(1), arcsin(x)))), `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))), x], []
`/`(`*`(`^`(x, 3), `*`(`^`(exp(1), 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
Main: Entering solver with 1 equation in 1 variable
radnormal: entering radnormal at time .249
Dispatch: dispatching to OnlyIn handler
Recurse: recursively solving 1 equations in 1 variables
Recurse: recursively solving 1 equations in 1 variables
Main: solving successful - now forming solutions
Main: Exiting solver returning 1 solution
simplify/do: applying simplify/trig function to expression
combine: combining with respect to trig
combine: combining with respect to trig
simplify/do: applying simplify/power function to expression
simplify/do: applying simplify/exp function to expression
{--> enter int:-ModuleApply, args = exp(u)*sin(u)^3*csgn(cos(u)), u
int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/indef2: invoking special integration procedure for csgn
int/indef1: first-stage indefinite integration
int/indef1: first-stage indefinite integration
int/indef2: second-stage indefinite integration
int/trigexp: case of integrand containing exp and trigs
<-- exit int:-ModuleApply (now in int/arctrig) = csgn(cos(u))*((1/10)*(sin(u)-3*cos(u))*exp(u)*sin(u)^2+(3/10)*exp(u)*(sin(u)-cos(u)))}
`+`(`*`(`/`(1, 10), `*`(`+`(x, `-`(`*`(3, `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))))), `*`(exp(arcsin(x)), `*`(`^`(x, 2))))), `*`(`/`(3, 10), `*`(exp(arcsin(x)), `*`(`+`(x, `-`(`*`(`^`(`+`(`-`...
`+`(`*`(`/`(1, 10), `*`(`+`(x, `-`(`*`(3, `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))))), `*`(exp(arcsin(x)), `*`(`^`(x, 2))))), `*`(`/`(3, 10), `*`(exp(arcsin(x)), `*`(`+`(x, `-`(`*`(`^`(`+`(`-`...
<-- exit Exact (now in Main) = (1/10)*(x-3*(-x^2+1)^(1/2))*exp(arcsin(x))*x^2+(3/10)*exp(arcsin(x))*(x-(-x^2+1)^(1/2))}
<-- exit Main (now in int:-ModuleApply) = (1/10)*(x-3*(-x^2+1)^(1/2))*exp(arcsin(x))*x^2+(3/10)*exp(arcsin(x))*(x-(-x^2+1)^(1/2))}
<-- exit int:-ModuleApply (now at top level) = (1/10)*(x-3*(-x^2+1)^(1/2))*exp(arcsin(x))*x^2+(3/10)*exp(arcsin(x))*(x-(-x^2+1)^(1/2))}
`+`(`*`(`/`(1, 10), `*`(`+`(x, `-`(`*`(3, `*`(`^`(`+`(`-`(`*`(`^`(x, 2))), 1), `/`(1, 2)))))), `*`(exp(arcsin(x)), `*`(`^`(x, 2))))), `*`(`/`(3, 10), `*`(exp(arcsin(x)), `*`(`+`(x, `-`(`*`(`^`(`+`(`-`... (1)
 

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