Optimal. Leaf size=22 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^6\right )}{6 a} \]
[Out]
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Rubi [A] time = 0.0331682, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^6\right )}{6 a} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a + b*x^6)),x]
[Out]
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Rubi in Sympy [A] time = 5.79293, size = 19, normalized size = 0.86 \[ \frac{\log{\left (x^{6} \right )}}{6 a} - \frac{\log{\left (a + b x^{6} \right )}}{6 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**6+a),x)
[Out]
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Mathematica [A] time = 0.0108346, size = 22, normalized size = 1. \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^6\right )}{6 a} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a + b*x^6)),x]
[Out]
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Maple [A] time = 0.006, size = 21, normalized size = 1. \[{\frac{\ln \left ( x \right ) }{a}}-{\frac{\ln \left ( b{x}^{6}+a \right ) }{6\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x^6+a),x)
[Out]
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Maxima [A] time = 1.44255, size = 31, normalized size = 1.41 \[ -\frac{\log \left (b x^{6} + a\right )}{6 \, a} + \frac{\log \left (x^{6}\right )}{6 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^6 + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218683, size = 24, normalized size = 1.09 \[ -\frac{\log \left (b x^{6} + a\right ) - 6 \, \log \left (x\right )}{6 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^6 + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.856905, size = 15, normalized size = 0.68 \[ \frac{\log{\left (x \right )}}{a} - \frac{\log{\left (\frac{a}{b} + x^{6} \right )}}{6 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**6+a),x)
[Out]
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GIAC/XCAS [A] time = 0.220296, size = 32, normalized size = 1.45 \[ \frac{{\rm ln}\left (x^{6}\right )}{6 \, a} - \frac{{\rm ln}\left ({\left | b x^{6} + a \right |}\right )}{6 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^6 + a)*x),x, algorithm="giac")
[Out]