Optimal. Leaf size=49 \[ -\frac{a^2 \log \left (a x^2+b\right )}{2 b^3}+\frac{a^2 \log (x)}{b^3}+\frac{a}{2 b^2 x^2}-\frac{1}{4 b x^4} \]
[Out]
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Rubi [A] time = 0.0841565, antiderivative size = 49, 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 \[ -\frac{a^2 \log \left (a x^2+b\right )}{2 b^3}+\frac{a^2 \log (x)}{b^3}+\frac{a}{2 b^2 x^2}-\frac{1}{4 b x^4} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)*x^7),x]
[Out]
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Rubi in Sympy [A] time = 12.3505, size = 48, normalized size = 0.98 \[ \frac{a^{2} \log{\left (x^{2} \right )}}{2 b^{3}} - \frac{a^{2} \log{\left (a x^{2} + b \right )}}{2 b^{3}} + \frac{a}{2 b^{2} x^{2}} - \frac{1}{4 b x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)/x**7,x)
[Out]
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Mathematica [A] time = 0.0125104, size = 49, normalized size = 1. \[ -\frac{a^2 \log \left (a x^2+b\right )}{2 b^3}+\frac{a^2 \log (x)}{b^3}+\frac{a}{2 b^2 x^2}-\frac{1}{4 b x^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)*x^7),x]
[Out]
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Maple [A] time = 0.009, size = 44, normalized size = 0.9 \[ -{\frac{1}{4\,b{x}^{4}}}+{\frac{a}{2\,{b}^{2}{x}^{2}}}+{\frac{{a}^{2}\ln \left ( x \right ) }{{b}^{3}}}-{\frac{{a}^{2}\ln \left ( a{x}^{2}+b \right ) }{2\,{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)/x^7,x)
[Out]
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Maxima [A] time = 1.43549, size = 63, normalized size = 1.29 \[ -\frac{a^{2} \log \left (a x^{2} + b\right )}{2 \, b^{3}} + \frac{a^{2} \log \left (x^{2}\right )}{2 \, b^{3}} + \frac{2 \, a x^{2} - b}{4 \, b^{2} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230024, size = 61, normalized size = 1.24 \[ -\frac{2 \, a^{2} x^{4} \log \left (a x^{2} + b\right ) - 4 \, a^{2} x^{4} \log \left (x\right ) - 2 \, a b x^{2} + b^{2}}{4 \, b^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.86721, size = 42, normalized size = 0.86 \[ \frac{a^{2} \log{\left (x \right )}}{b^{3}} - \frac{a^{2} \log{\left (x^{2} + \frac{b}{a} \right )}}{2 b^{3}} + \frac{2 a x^{2} - b}{4 b^{2} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.222999, size = 77, normalized size = 1.57 \[ \frac{a^{2}{\rm ln}\left (x^{2}\right )}{2 \, b^{3}} - \frac{a^{2}{\rm ln}\left ({\left | a x^{2} + b \right |}\right )}{2 \, b^{3}} - \frac{3 \, a^{2} x^{4} - 2 \, a b x^{2} + b^{2}}{4 \, b^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)*x^7),x, algorithm="giac")
[Out]