Optimal. Leaf size=29 \[ \frac{\tan ^{-1}\left (\frac{\sqrt{b} x^3}{\sqrt{a}}\right )}{3 \sqrt{a} \sqrt{b}} \]
[Out]
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Rubi [A] time = 0.0372156, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\tan ^{-1}\left (\frac{\sqrt{b} x^3}{\sqrt{a}}\right )}{3 \sqrt{a} \sqrt{b}} \]
Antiderivative was successfully verified.
[In] Int[x^2/(a + b*x^6),x]
[Out]
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Rubi in Sympy [A] time = 5.14479, size = 26, normalized size = 0.9 \[ \frac{\operatorname{atan}{\left (\frac{\sqrt{b} x^{3}}{\sqrt{a}} \right )}}{3 \sqrt{a} \sqrt{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(b*x**6+a),x)
[Out]
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Mathematica [A] time = 0.0111824, size = 29, normalized size = 1. \[ \frac{\tan ^{-1}\left (\frac{\sqrt{b} x^3}{\sqrt{a}}\right )}{3 \sqrt{a} \sqrt{b}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(a + b*x^6),x]
[Out]
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Maple [A] time = 0.002, size = 19, normalized size = 0.7 \[{\frac{1}{3}\arctan \left ({b{x}^{3}{\frac{1}{\sqrt{ab}}}} \right ){\frac{1}{\sqrt{ab}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(b*x^6+a),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^6 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225422, size = 1, normalized size = 0.03 \[ \left [\frac{\log \left (\frac{2 \, a b x^{3} +{\left (b x^{6} - a\right )} \sqrt{-a b}}{b x^{6} + a}\right )}{6 \, \sqrt{-a b}}, \frac{\arctan \left (\frac{\sqrt{a b} x^{3}}{a}\right )}{3 \, \sqrt{a b}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^6 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.545832, size = 56, normalized size = 1.93 \[ - \frac{\sqrt{- \frac{1}{a b}} \log{\left (- a \sqrt{- \frac{1}{a b}} + x^{3} \right )}}{6} + \frac{\sqrt{- \frac{1}{a b}} \log{\left (a \sqrt{- \frac{1}{a b}} + x^{3} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(b*x**6+a),x)
[Out]
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GIAC/XCAS [A] time = 0.224465, size = 24, normalized size = 0.83 \[ \frac{\arctan \left (\frac{b x^{3}}{\sqrt{a b}}\right )}{3 \, \sqrt{a b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(b*x^6 + a),x, algorithm="giac")
[Out]