Optimal. Leaf size=15 \[ -\frac{\log \left (a+\frac{b}{x^2}\right )}{2 b} \]
[Out]
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Rubi [A] time = 0.0183334, 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 \[ -\frac{\log \left (a+\frac{b}{x^2}\right )}{2 b} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)*x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.12996, size = 12, normalized size = 0.8 \[ - \frac{\log{\left (a + \frac{b}{x^{2}} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)/x**3,x)
[Out]
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Mathematica [A] time = 0.00962509, size = 22, normalized size = 1.47 \[ \frac{\log (x)}{b}-\frac{\log \left (a x^2+b\right )}{2 b} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)*x^3),x]
[Out]
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Maple [A] time = 0.005, size = 21, normalized size = 1.4 \[{\frac{\ln \left ( x \right ) }{b}}-{\frac{\ln \left ( a{x}^{2}+b \right ) }{2\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)/x^3,x)
[Out]
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Maxima [A] time = 1.42265, size = 18, normalized size = 1.2 \[ -\frac{\log \left (a + \frac{b}{x^{2}}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226803, size = 24, normalized size = 1.6 \[ -\frac{\log \left (a x^{2} + b\right ) - 2 \, \log \left (x\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.527612, size = 15, normalized size = 1. \[ \frac{\log{\left (x \right )}}{b} - \frac{\log{\left (x^{2} + \frac{b}{a} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.225048, size = 32, normalized size = 2.13 \[ \frac{{\rm ln}\left (x^{2}\right )}{2 \, b} - \frac{{\rm ln}\left ({\left | a x^{2} + b \right |}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^3),x, algorithm="giac")
[Out]