Optimal. Leaf size=14 \[ -\frac{1}{4 x^4 \left (x^2+1\right )^2} \]
[Out]
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Rubi [A] time = 0.0097358, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{1}{4 x^4 \left (x^2+1\right )^2} \]
Antiderivative was successfully verified.
[In] Int[(1 + 2*x^2)/(x^5*(1 + x^2)^3),x]
[Out]
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Rubi in Sympy [A] time = 6.69551, size = 14, normalized size = 1. \[ - \frac{1}{4 x^{4} \left (x^{2} + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**2+1)/x**5/(x**2+1)**3,x)
[Out]
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Mathematica [A] time = 0.00977804, size = 14, normalized size = 1. \[ -\frac{1}{4 x^4 \left (x^2+1\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 2*x^2)/(x^5*(1 + x^2)^3),x]
[Out]
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Maple [B] time = 0.016, size = 30, normalized size = 2.1 \[ -{\frac{1}{4\,{x}^{4}}}+{\frac{1}{2\,{x}^{2}}}-{\frac{1}{4\, \left ({x}^{2}+1 \right ) ^{2}}}-{\frac{1}{2\,{x}^{2}+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^2+1)/x^5/(x^2+1)^3,x)
[Out]
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Maxima [A] time = 1.34297, size = 22, normalized size = 1.57 \[ -\frac{1}{4 \,{\left (x^{8} + 2 \, x^{6} + x^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 1)/((x^2 + 1)^3*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203568, size = 22, normalized size = 1.57 \[ -\frac{1}{4 \,{\left (x^{8} + 2 \, x^{6} + x^{4}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 1)/((x^2 + 1)^3*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.357549, size = 17, normalized size = 1.21 \[ - \frac{1}{4 x^{8} + 8 x^{6} + 4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**2+1)/x**5/(x**2+1)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.227022, size = 15, normalized size = 1.07 \[ -\frac{1}{4 \,{\left (x^{4} + x^{2}\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 + 1)/((x^2 + 1)^3*x^5),x, algorithm="giac")
[Out]