Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^6\right )}{6 b} \]
[Out]
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Rubi [A] time = 0.0094443, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\log \left (a+b x^6\right )}{6 b} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a + b*x^6),x]
[Out]
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Rubi in Sympy [A] time = 2.17189, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{6} \right )}}{6 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**6+a),x)
[Out]
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Mathematica [A] time = 0.00649054, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^6\right )}{6 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a + b*x^6),x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( b{x}^{6}+a \right ) }{6\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^6+a),x)
[Out]
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Maxima [A] time = 1.43629, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{6} + a\right )}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^6 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212859, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{6} + a\right )}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^6 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.515937, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{6} \right )}}{6 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**6+a),x)
[Out]
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GIAC/XCAS [A] time = 0.2264, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | b x^{6} + a \right |}\right )}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^6 + a),x, algorithm="giac")
[Out]