Optimal. Leaf size=35 \[ \frac{a \log \left (a x^2+b\right )}{2 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{2 b x^2} \]
[Out]
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Rubi [A] time = 0.0688594, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{a \log \left (a x^2+b\right )}{2 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{2 b x^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)*x^5),x]
[Out]
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Rubi in Sympy [A] time = 9.68781, size = 34, normalized size = 0.97 \[ - \frac{a \log{\left (x^{2} \right )}}{2 b^{2}} + \frac{a \log{\left (a x^{2} + b \right )}}{2 b^{2}} - \frac{1}{2 b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)/x**5,x)
[Out]
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Mathematica [A] time = 0.0119715, size = 35, normalized size = 1. \[ \frac{a \log \left (a x^2+b\right )}{2 b^2}-\frac{a \log (x)}{b^2}-\frac{1}{2 b x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)*x^5),x]
[Out]
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Maple [A] time = 0.009, size = 32, normalized size = 0.9 \[ -{\frac{1}{2\,b{x}^{2}}}-{\frac{a\ln \left ( x \right ) }{{b}^{2}}}+{\frac{a\ln \left ( a{x}^{2}+b \right ) }{2\,{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)/x^5,x)
[Out]
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Maxima [A] time = 1.54631, size = 45, normalized size = 1.29 \[ \frac{a \log \left (a x^{2} + b\right )}{2 \, b^{2}} - \frac{a \log \left (x^{2}\right )}{2 \, b^{2}} - \frac{1}{2 \, b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237591, size = 45, normalized size = 1.29 \[ \frac{a x^{2} \log \left (a x^{2} + b\right ) - 2 \, a x^{2} \log \left (x\right ) - b}{2 \, b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.57859, size = 31, normalized size = 0.89 \[ - \frac{a \log{\left (x \right )}}{b^{2}} + \frac{a \log{\left (x^{2} + \frac{b}{a} \right )}}{2 b^{2}} - \frac{1}{2 b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.225572, size = 58, normalized size = 1.66 \[ -\frac{a{\rm ln}\left (x^{2}\right )}{2 \, b^{2}} + \frac{a{\rm ln}\left ({\left | a x^{2} + b \right |}\right )}{2 \, b^{2}} + \frac{a x^{2} - b}{2 \, b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^5),x, algorithm="giac")
[Out]