Optimal. Leaf size=8 \[ \frac{1}{2} \tan ^{-1}\left (x^2\right ) \]
[Out]
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Rubi [A] time = 0.00874866, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{1}{2} \tan ^{-1}\left (x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[x/(1 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 1.06419, size = 5, normalized size = 0.62 \[ \frac{\operatorname{atan}{\left (x^{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**4+1),x)
[Out]
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Mathematica [A] time = 0.00453224, size = 8, normalized size = 1. \[ \frac{1}{2} \tan ^{-1}\left (x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 + x^4),x]
[Out]
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Maple [A] time = 0.003, size = 7, normalized size = 0.9 \[{\frac{\arctan \left ({x}^{2} \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^4+1),x)
[Out]
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Maxima [A] time = 1.54005, size = 8, normalized size = 1. \[ \frac{1}{2} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203921, size = 8, normalized size = 1. \[ \frac{1}{2} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.087924, size = 5, normalized size = 0.62 \[ \frac{\operatorname{atan}{\left (x^{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**4+1),x)
[Out]
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GIAC/XCAS [A] time = 0.205238, size = 8, normalized size = 1. \[ \frac{1}{2} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 1),x, algorithm="giac")
[Out]