Optimal. Leaf size=17 \[ x-\frac{1}{x}-\frac{10}{3} \tan ^{-1}\left (\frac{x}{3}\right ) \]
[Out]
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Rubi [A] time = 0.0415431, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ x-\frac{1}{x}-\frac{10}{3} \tan ^{-1}\left (\frac{x}{3}\right ) \]
Antiderivative was successfully verified.
[In] Int[(9 + x^4)/(x^2*(9 + x^2)),x]
[Out]
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Rubi in Sympy [A] time = 6.98288, size = 12, normalized size = 0.71 \[ x - \frac{10 \operatorname{atan}{\left (\frac{x}{3} \right )}}{3} - \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**4+9)/x**2/(x**2+9),x)
[Out]
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Mathematica [A] time = 0.00869106, size = 17, normalized size = 1. \[ x-\frac{1}{x}-\frac{10}{3} \tan ^{-1}\left (\frac{x}{3}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(9 + x^4)/(x^2*(9 + x^2)),x]
[Out]
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Maple [A] time = 0.009, size = 14, normalized size = 0.8 \[ -{x}^{-1}+x-{\frac{10}{3}\arctan \left ({\frac{x}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^4+9)/x^2/(x^2+9),x)
[Out]
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Maxima [A] time = 0.88416, size = 18, normalized size = 1.06 \[ x - \frac{1}{x} - \frac{10}{3} \, \arctan \left (\frac{1}{3} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 9)/((x^2 + 9)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.252626, size = 26, normalized size = 1.53 \[ \frac{3 \, x^{2} - 10 \, x \arctan \left (\frac{1}{3} \, x\right ) - 3}{3 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 9)/((x^2 + 9)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.208994, size = 12, normalized size = 0.71 \[ x - \frac{10 \operatorname{atan}{\left (\frac{x}{3} \right )}}{3} - \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**4+9)/x**2/(x**2+9),x)
[Out]
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GIAC/XCAS [A] time = 0.259991, size = 18, normalized size = 1.06 \[ x - \frac{1}{x} - \frac{10}{3} \, \arctan \left (\frac{1}{3} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + 9)/((x^2 + 9)*x^2),x, algorithm="giac")
[Out]