Optimal. Leaf size=22 \[ \tan ^{-1}\left (\frac{x}{2}\right )-\frac{3 \tan ^{-1}\left (\sqrt{2} x\right )}{\sqrt{2}} \]
[Out]
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Rubi [A] time = 0.031989, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \tan ^{-1}\left (\frac{x}{2}\right )-\frac{3 \tan ^{-1}\left (\sqrt{2} x\right )}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Int[(-10 + x^2)/(4 + 9*x^2 + 2*x^4),x]
[Out]
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Rubi in Sympy [A] time = 8.63619, size = 20, normalized size = 0.91 \[ \operatorname{atan}{\left (\frac{x}{2} \right )} - \frac{3 \sqrt{2} \operatorname{atan}{\left (\sqrt{2} x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-10)/(2*x**4+9*x**2+4),x)
[Out]
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Mathematica [A] time = 0.0196729, size = 22, normalized size = 1. \[ \tan ^{-1}\left (\frac{x}{2}\right )-\frac{3 \tan ^{-1}\left (\sqrt{2} x\right )}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Integrate[(-10 + x^2)/(4 + 9*x^2 + 2*x^4),x]
[Out]
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Maple [A] time = 0.01, size = 17, normalized size = 0.8 \[ \arctan \left ({\frac{x}{2}} \right ) -{\frac{3\,\arctan \left ( \sqrt{2}x \right ) \sqrt{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-10)/(2*x^4+9*x^2+4),x)
[Out]
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Maxima [A] time = 0.857709, size = 22, normalized size = 1. \[ -\frac{3}{2} \, \sqrt{2} \arctan \left (\sqrt{2} x\right ) + \arctan \left (\frac{1}{2} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 10)/(2*x^4 + 9*x^2 + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265483, size = 30, normalized size = 1.36 \[ \frac{1}{2} \, \sqrt{2}{\left (\sqrt{2} \arctan \left (\frac{1}{2} \, x\right ) - 3 \, \arctan \left (\sqrt{2} x\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 10)/(2*x^4 + 9*x^2 + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.411319, size = 20, normalized size = 0.91 \[ \operatorname{atan}{\left (\frac{x}{2} \right )} - \frac{3 \sqrt{2} \operatorname{atan}{\left (\sqrt{2} x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-10)/(2*x**4+9*x**2+4),x)
[Out]
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GIAC/XCAS [A] time = 0.259908, size = 22, normalized size = 1. \[ -\frac{3}{2} \, \sqrt{2} \arctan \left (\sqrt{2} x\right ) + \arctan \left (\frac{1}{2} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 10)/(2*x^4 + 9*x^2 + 4),x, algorithm="giac")
[Out]