Optimal. Leaf size=27 \[ \frac{-5 x^6+x^4+5 x^2-3 x+2}{\left (x^4+x+3\right )^3} \]
[Out]
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Rubi [F] time = 0.54944, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{3 \left (-47+228 x+120 x^2+19 x^3\right )}{\left (3+x+x^4\right )^4}+\frac{42-320 x-75 x^2-8 x^3}{\left (3+x+x^4\right )^3}+\frac{30 x}{\left (3+x+x^4\right )^2},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(3*(-47 + 228*x + 120*x^2 + 19*x^3))/(3 + x + x^4)^4 + (42 - 320*x - 75*x^2 - 8*x^3)/(3 + x + x^4)^3 + (30*x)/(3 + x + x^4)^2,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(3*(19*x**3+120*x**2+228*x-47)/(x**4+x+3)**4+(-8*x**3-75*x**2-320*x+42)/(x**4+x+3)**3+30*x/(x**4+x+3)**2,x)
[Out]
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Mathematica [A] time = 0.0144376, size = 27, normalized size = 1. \[ \frac{-5 x^6+x^4+5 x^2-3 x+2}{\left (x^4+x+3\right )^3} \]
Antiderivative was successfully verified.
[In] Integrate[(3*(-47 + 228*x + 120*x^2 + 19*x^3))/(3 + x + x^4)^4 + (42 - 320*x - 75*x^2 - 8*x^3)/(3 + x + x^4)^3 + (30*x)/(3 + x + x^4)^2,x]
[Out]
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Maple [C] time = 0.04, size = 250, normalized size = 9.3 \[{\frac{1}{ \left ({x}^{4}+x+3 \right ) ^{2}} \left ({\frac{377432\,{x}^{7}}{195075}}-{\frac{1404328\,{x}^{6}}{195075}}+{\frac{234517\,{x}^{5}}{195075}}+{\frac{660506\,{x}^{4}}{195075}}-{\frac{208792\,{x}^{3}}{195075}}-{\frac{13339729\,{x}^{2}}{390150}}+{\frac{89881\,x}{13005}}+{\frac{121303}{21675}} \right ) }+{\frac{1}{195075}\sum _{{\it \_R}={\it RootOf} \left ({{\it \_Z}}^{4}+{\it \_Z}+3 \right ) }{\frac{ \left ( 377432\,{{\it \_R}}^{2}-2808656\,{\it \_R}+703551 \right ) \ln \left ( x-{\it \_R} \right ) }{4\,{{\it \_R}}^{3}+1}}}+30\,{\frac{1}{{x}^{4}+x+3} \left ( -{\frac{16\,{x}^{3}}{765}}+{\frac{64\,{x}^{2}}{765}}-{\frac{x}{765}}-{\frac{4}{255}} \right ) }+{\frac{2}{51}\sum _{{\it \_R}={\it RootOf} \left ({{\it \_Z}}^{4}+{\it \_Z}+3 \right ) }{\frac{ \left ( -16\,{{\it \_R}}^{2}+128\,{\it \_R}-3 \right ) \ln \left ( x-{\it \_R} \right ) }{4\,{{\it \_R}}^{3}+1}}}+3\,{\frac{1}{ \left ({x}^{4}+x+3 \right ) ^{3}} \left ( -{\frac{255032\,{x}^{11}}{585225}}+{\frac{914728\,{x}^{10}}{585225}}-{\frac{226867\,{x}^{9}}{585225}}-{\frac{701338\,{x}^{8}}{585225}}+{\frac{236024\,{x}^{7}}{585225}}+{\frac{13501313\,{x}^{6}}{1170450}}-{\frac{2360372\,{x}^{5}}{585225}}-{\frac{1873778\,{x}^{4}}{585225}}+{\frac{10935781\,{x}^{3}}{1170450}}+{\frac{3415123\,{x}^{2}}{130050}}-{\frac{62987\,x}{7225}}-{\frac{76253}{21675}} \right ) }+{\frac{1}{195075}\sum _{{\it \_R}={\it RootOf} \left ({{\it \_Z}}^{4}+{\it \_Z}+3 \right ) }{\frac{ \left ( -255032\,{{\it \_R}}^{2}+1829456\,{\it \_R}-680601 \right ) \ln \left ( x-{\it \_R} \right ) }{4\,{{\it \_R}}^{3}+1}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(3*(19*x^3+120*x^2+228*x-47)/(x^4+x+3)^4+(-8*x^3-75*x^2-320*x+42)/(x^4+x+3)^3+30*x/(x^4+x+3)^2,x)
[Out]
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Maxima [A] time = 0.81328, size = 88, normalized size = 3.26 \[ -\frac{5 \, x^{6} - x^{4} - 5 \, x^{2} + 3 \, x - 2}{x^{12} + 3 \, x^{9} + 9 \, x^{8} + 3 \, x^{6} + 18 \, x^{5} + 27 \, x^{4} + x^{3} + 9 \, x^{2} + 27 \, x + 27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(30*x/(x^4 + x + 3)^2 - (8*x^3 + 75*x^2 + 320*x - 42)/(x^4 + x + 3)^3 + 3*(19*x^3 + 120*x^2 + 228*x - 47)/(x^4 + x + 3)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25761, size = 88, normalized size = 3.26 \[ -\frac{5 \, x^{6} - x^{4} - 5 \, x^{2} + 3 \, x - 2}{x^{12} + 3 \, x^{9} + 9 \, x^{8} + 3 \, x^{6} + 18 \, x^{5} + 27 \, x^{4} + x^{3} + 9 \, x^{2} + 27 \, x + 27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(30*x/(x^4 + x + 3)^2 - (8*x^3 + 75*x^2 + 320*x - 42)/(x^4 + x + 3)^3 + 3*(19*x^3 + 120*x^2 + 228*x - 47)/(x^4 + x + 3)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.06688, size = 61, normalized size = 2.26 \[ - \frac{5 x^{6} - x^{4} - 5 x^{2} + 3 x - 2}{x^{12} + 3 x^{9} + 9 x^{8} + 3 x^{6} + 18 x^{5} + 27 x^{4} + x^{3} + 9 x^{2} + 27 x + 27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(3*(19*x**3+120*x**2+228*x-47)/(x**4+x+3)**4+(-8*x**3-75*x**2-320*x+42)/(x**4+x+3)**3+30*x/(x**4+x+3)**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{30 \, x}{{\left (x^{4} + x + 3\right )}^{2}} - \frac{8 \, x^{3} + 75 \, x^{2} + 320 \, x - 42}{{\left (x^{4} + x + 3\right )}^{3}} + \frac{3 \,{\left (19 \, x^{3} + 120 \, x^{2} + 228 \, x - 47\right )}}{{\left (x^{4} + x + 3\right )}^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(30*x/(x^4 + x + 3)^2 - (8*x^3 + 75*x^2 + 320*x - 42)/(x^4 + x + 3)^3 + 3*(19*x^3 + 120*x^2 + 228*x - 47)/(x^4 + x + 3)^4,x, algorithm="giac")
[Out]