Optimal. Leaf size=15 \[ \frac{\log \left (a x^4+b\right )}{4 a} \]
[Out]
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Rubi [A] time = 0.00945454, 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 \[ \frac{\log \left (a x^4+b\right )}{4 a} \]
Antiderivative was successfully verified.
[In] Int[(b/x^3 + a*x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 2.54026, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a x^{4} + b \right )}}{4 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**3+a*x),x)
[Out]
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Mathematica [A] time = 0.00686364, size = 15, normalized size = 1. \[ \frac{\log \left (a x^4+b\right )}{4 a} \]
Antiderivative was successfully verified.
[In] Integrate[(b/x^3 + a*x)^(-1),x]
[Out]
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Maple [A] time = 0.001, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( a{x}^{4}+b \right ) }{4\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^3+a*x),x)
[Out]
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Maxima [A] time = 1.37943, size = 18, normalized size = 1.2 \[ \frac{\log \left (a x^{4} + b\right )}{4 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x + b/x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209262, size = 18, normalized size = 1.2 \[ \frac{\log \left (a x^{4} + b\right )}{4 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x + b/x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.365069, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a x^{4} + b \right )}}{4 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x**3+a*x),x)
[Out]
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GIAC/XCAS [A] time = 0.218496, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | a x^{4} + b \right |}\right )}{4 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a*x + b/x^3),x, algorithm="giac")
[Out]