Optimal. Leaf size=69 \[ -\frac{4 a^3 \log (x)}{b^5}+\frac{4 a^3 \log (a x+b)}{b^5}-\frac{a^3}{b^4 (a x+b)}-\frac{3 a^2}{b^4 x}+\frac{a}{b^3 x^2}-\frac{1}{3 b^2 x^3} \]
[Out]
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Rubi [A] time = 0.101989, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{4 a^3 \log (x)}{b^5}+\frac{4 a^3 \log (a x+b)}{b^5}-\frac{a^3}{b^4 (a x+b)}-\frac{3 a^2}{b^4 x}+\frac{a}{b^3 x^2}-\frac{1}{3 b^2 x^3} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^2*x^6),x]
[Out]
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Rubi in Sympy [A] time = 14.4772, size = 66, normalized size = 0.96 \[ - \frac{a^{3}}{b^{4} \left (a x + b\right )} - \frac{4 a^{3} \log{\left (x \right )}}{b^{5}} + \frac{4 a^{3} \log{\left (a x + b \right )}}{b^{5}} - \frac{3 a^{2}}{b^{4} x} + \frac{a}{b^{3} x^{2}} - \frac{1}{3 b^{2} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**2/x**6,x)
[Out]
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Mathematica [A] time = 0.096982, size = 66, normalized size = 0.96 \[ -\frac{-12 a^3 \log (a x+b)+12 a^3 \log (x)+\frac{b \left (12 a^3 x^3+6 a^2 b x^2-2 a b^2 x+b^3\right )}{x^3 (a x+b)}}{3 b^5} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^2*x^6),x]
[Out]
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Maple [A] time = 0.017, size = 68, normalized size = 1. \[ -{\frac{1}{3\,{b}^{2}{x}^{3}}}+{\frac{a}{{b}^{3}{x}^{2}}}-3\,{\frac{{a}^{2}}{{b}^{4}x}}-{\frac{{a}^{3}}{{b}^{4} \left ( ax+b \right ) }}-4\,{\frac{{a}^{3}\ln \left ( x \right ) }{{b}^{5}}}+4\,{\frac{{a}^{3}\ln \left ( ax+b \right ) }{{b}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^2/x^6,x)
[Out]
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Maxima [A] time = 1.44179, size = 99, normalized size = 1.43 \[ -\frac{12 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} - 2 \, a b^{2} x + b^{3}}{3 \,{\left (a b^{4} x^{4} + b^{5} x^{3}\right )}} + \frac{4 \, a^{3} \log \left (a x + b\right )}{b^{5}} - \frac{4 \, a^{3} \log \left (x\right )}{b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227271, size = 128, normalized size = 1.86 \[ -\frac{12 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 2 \, a b^{3} x + b^{4} - 12 \,{\left (a^{4} x^{4} + a^{3} b x^{3}\right )} \log \left (a x + b\right ) + 12 \,{\left (a^{4} x^{4} + a^{3} b x^{3}\right )} \log \left (x\right )}{3 \,{\left (a b^{5} x^{4} + b^{6} x^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.87241, size = 66, normalized size = 0.96 \[ \frac{4 a^{3} \left (- \log{\left (x \right )} + \log{\left (x + \frac{b}{a} \right )}\right )}{b^{5}} - \frac{12 a^{3} x^{3} + 6 a^{2} b x^{2} - 2 a b^{2} x + b^{3}}{3 a b^{4} x^{4} + 3 b^{5} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**2/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.229466, size = 99, normalized size = 1.43 \[ \frac{4 \, a^{3}{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{5}} - \frac{4 \, a^{3}{\rm ln}\left ({\left | x \right |}\right )}{b^{5}} - \frac{12 \, a^{3} b x^{3} + 6 \, a^{2} b^{2} x^{2} - 2 \, a b^{3} x + b^{4}}{3 \,{\left (a x + b\right )} b^{5} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^6),x, algorithm="giac")
[Out]