Optimal. Leaf size=22 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^3\right )}{3 a} \]
[Out]
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Rubi [A] time = 0.0378885, 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 \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^3\right )}{3 a} \]
Antiderivative was successfully verified.
[In] Int[1/(x*(a + b*x^3)),x]
[Out]
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Rubi in Sympy [A] time = 5.43752, size = 19, normalized size = 0.86 \[ \frac{\log{\left (x^{3} \right )}}{3 a} - \frac{\log{\left (a + b x^{3} \right )}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x**3+a),x)
[Out]
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Mathematica [A] time = 0.00889521, size = 22, normalized size = 1. \[ \frac{\log (x)}{a}-\frac{\log \left (a+b x^3\right )}{3 a} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(a + b*x^3)),x]
[Out]
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Maple [A] time = 0.001, size = 21, normalized size = 1. \[{\frac{\ln \left ( x \right ) }{a}}-{\frac{\ln \left ( b{x}^{3}+a \right ) }{3\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x^3+a),x)
[Out]
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Maxima [A] time = 1.34389, size = 31, normalized size = 1.41 \[ -\frac{\log \left (b x^{3} + a\right )}{3 \, a} + \frac{\log \left (x^{3}\right )}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216405, size = 24, normalized size = 1.09 \[ -\frac{\log \left (b x^{3} + a\right ) - 3 \, \log \left (x\right )}{3 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.572219, size = 15, normalized size = 0.68 \[ \frac{\log{\left (x \right )}}{a} - \frac{\log{\left (\frac{a}{b} + x^{3} \right )}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x**3+a),x)
[Out]
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GIAC/XCAS [A] time = 0.217243, size = 30, normalized size = 1.36 \[ -\frac{{\rm ln}\left ({\left | b x^{3} + a \right |}\right )}{3 \, a} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)*x),x, algorithm="giac")
[Out]