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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

{--> enter exp, args = 1
<-- exit exp (now at top level) = exp(1)} {--> 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 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(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
{--> enter unknown, args = exp(1)
<-- 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))))}
<-- 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(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]
<-- 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
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)))}
<-- 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)

 

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