Optimal. Leaf size=38 \[ -\frac{\log \left (a x^2+b\right )}{2 b^2}+\frac{1}{2 b \left (a x^2+b\right )}+\frac{\log (x)}{b^2} \]
[Out]
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Rubi [A] time = 0.0757825, antiderivative size = 38, 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 \[ -\frac{\log \left (a x^2+b\right )}{2 b^2}+\frac{1}{2 b \left (a x^2+b\right )}+\frac{\log (x)}{b^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)^2*x^5),x]
[Out]
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Rubi in Sympy [A] time = 10.0786, size = 34, normalized size = 0.89 \[ \frac{1}{2 b \left (a x^{2} + b\right )} + \frac{\log{\left (x^{2} \right )}}{2 b^{2}} - \frac{\log{\left (a x^{2} + b \right )}}{2 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**2/x**5,x)
[Out]
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Mathematica [A] time = 0.023608, size = 33, normalized size = 0.87 \[ \frac{\frac{b}{a x^2+b}-\log \left (a x^2+b\right )+2 \log (x)}{2 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)^2*x^5),x]
[Out]
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Maple [A] time = 0.015, size = 35, normalized size = 0.9 \[{\frac{1}{2\,b \left ( a{x}^{2}+b \right ) }}+{\frac{\ln \left ( x \right ) }{{b}^{2}}}-{\frac{\ln \left ( a{x}^{2}+b \right ) }{2\,{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^2/x^5,x)
[Out]
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Maxima [A] time = 1.43685, size = 50, normalized size = 1.32 \[ \frac{1}{2 \,{\left (a b x^{2} + b^{2}\right )}} - \frac{\log \left (a x^{2} + b\right )}{2 \, b^{2}} + \frac{\log \left (x^{2}\right )}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^2*x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240162, size = 63, normalized size = 1.66 \[ -\frac{{\left (a x^{2} + b\right )} \log \left (a x^{2} + b\right ) - 2 \,{\left (a x^{2} + b\right )} \log \left (x\right ) - b}{2 \,{\left (a b^{2} x^{2} + b^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^2*x^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.69092, size = 34, normalized size = 0.89 \[ \frac{1}{2 a b x^{2} + 2 b^{2}} + \frac{\log{\left (x \right )}}{b^{2}} - \frac{\log{\left (x^{2} + \frac{b}{a} \right )}}{2 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**2/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.228627, size = 63, normalized size = 1.66 \[ \frac{{\rm ln}\left (x^{2}\right )}{2 \, b^{2}} - \frac{{\rm ln}\left ({\left | a x^{2} + b \right |}\right )}{2 \, b^{2}} + \frac{a x^{2} + 2 \, b}{2 \,{\left (a x^{2} + b\right )} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^2*x^5),x, algorithm="giac")
[Out]