Optimal. Leaf size=15 \[ \frac{\tan ^{-1}\left (\frac{x^2}{a^2}\right )}{2 a^2} \]
[Out]
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Rubi [A] time = 0.0165114, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{\tan ^{-1}\left (\frac{x^2}{a^2}\right )}{2 a^2} \]
Antiderivative was successfully verified.
[In] Int[x/(a^4 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 1.59015, size = 12, normalized size = 0.8 \[ \frac{\operatorname{atan}{\left (\frac{x^{2}}{a^{2}} \right )}}{2 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(a**4+x**4),x)
[Out]
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Mathematica [A] time = 0.00483174, size = 15, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{x^2}{a^2}\right )}{2 a^2} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a^4 + x^4),x]
[Out]
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Maple [A] time = 0.006, size = 14, normalized size = 0.9 \[{\frac{1}{2\,{a}^{2}}\arctan \left ({\frac{{x}^{2}}{{a}^{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(a^4+x^4),x)
[Out]
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Maxima [A] time = 1.48336, size = 18, normalized size = 1.2 \[ \frac{\arctan \left (\frac{x^{2}}{a^{2}}\right )}{2 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a^4 + x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.195442, size = 18, normalized size = 1.2 \[ \frac{\arctan \left (\frac{x^{2}}{a^{2}}\right )}{2 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a^4 + x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.154332, size = 29, normalized size = 1.93 \[ \frac{- \frac{i \log{\left (- i a^{2} + x^{2} \right )}}{4} + \frac{i \log{\left (i a^{2} + x^{2} \right )}}{4}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a**4+x**4),x)
[Out]
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GIAC/XCAS [A] time = 0.201055, size = 18, normalized size = 1.2 \[ \frac{\arctan \left (\frac{x^{2}}{a^{2}}\right )}{2 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a^4 + x^4),x, algorithm="giac")
[Out]