Optimal. Leaf size=13 \[ -\frac{1}{4 \left (x^4+x^2\right )^2} \]
[Out]
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Rubi [A] time = 0.0083106, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{1}{4 \left (x^4+x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Int[(x + 2*x^3)/(x^2 + x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 8.47684, size = 14, normalized size = 1.08 \[ - \frac{1}{4 x^{4} \left (x^{2} + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**3+x)/(x**4+x**2)**3,x)
[Out]
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Mathematica [A] time = 0.0102078, size = 14, normalized size = 1.08 \[ -\frac{1}{4 x^4 \left (x^2+1\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[(x + 2*x^3)/(x^2 + x^4)^3,x]
[Out]
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Maple [B] time = 0.017, size = 30, normalized size = 2.3 \[ -{\frac{1}{4\,{x}^{4}}}+{\frac{1}{2\,{x}^{2}}}-{\frac{1}{4\, \left ({x}^{2}+1 \right ) ^{2}}}-{\frac{1}{2\,{x}^{2}+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^3+x)/(x^4+x^2)^3,x)
[Out]
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Maxima [A] time = 0.788247, size = 15, normalized size = 1.15 \[ -\frac{1}{4 \,{\left (x^{4} + x^{2}\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^3 + x)/(x^4 + x^2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244984, size = 22, normalized size = 1.69 \[ -\frac{1}{4 \,{\left (x^{8} + 2 \, x^{6} + x^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^3 + x)/(x^4 + x^2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.367543, size = 17, normalized size = 1.31 \[ - \frac{1}{4 x^{8} + 8 x^{6} + 4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**3+x)/(x**4+x**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.259861, size = 15, normalized size = 1.15 \[ -\frac{1}{4 \,{\left (x^{4} + x^{2}\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^3 + x)/(x^4 + x^2)^3,x, algorithm="giac")
[Out]