Optimal. Leaf size=81 \[ -\frac{b^6}{a^7 (a x+b)}-\frac{6 b^5 \log (a x+b)}{a^7}+\frac{5 b^4 x}{a^6}-\frac{2 b^3 x^2}{a^5}+\frac{b^2 x^3}{a^4}-\frac{b x^4}{2 a^3}+\frac{x^5}{5 a^2} \]
[Out]
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Rubi [A] time = 0.132517, antiderivative size = 81, 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 \[ -\frac{b^6}{a^7 (a x+b)}-\frac{6 b^5 \log (a x+b)}{a^7}+\frac{5 b^4 x}{a^6}-\frac{2 b^3 x^2}{a^5}+\frac{b^2 x^3}{a^4}-\frac{b x^4}{2 a^3}+\frac{x^5}{5 a^2} \]
Antiderivative was successfully verified.
[In] Int[x^4/(a + b/x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{5}}{5 a^{2}} - \frac{b x^{4}}{2 a^{3}} + \frac{b^{2} x^{3}}{a^{4}} - \frac{4 b^{3} \int x\, dx}{a^{5}} + \frac{5 b^{4} x}{a^{6}} - \frac{b^{6}}{a^{7} \left (a x + b\right )} - \frac{6 b^{5} \log{\left (a x + b \right )}}{a^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(a+b/x)**2,x)
[Out]
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Mathematica [A] time = 0.0419293, size = 77, normalized size = 0.95 \[ \frac{2 a^5 x^5-5 a^4 b x^4+10 a^3 b^2 x^3-20 a^2 b^3 x^2-\frac{10 b^6}{a x+b}-60 b^5 \log (a x+b)+50 a b^4 x}{10 a^7} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(a + b/x)^2,x]
[Out]
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Maple [A] time = 0.011, size = 78, normalized size = 1. \[ 5\,{\frac{{b}^{4}x}{{a}^{6}}}-2\,{\frac{{b}^{3}{x}^{2}}{{a}^{5}}}+{\frac{{b}^{2}{x}^{3}}{{a}^{4}}}-{\frac{b{x}^{4}}{2\,{a}^{3}}}+{\frac{{x}^{5}}{5\,{a}^{2}}}-{\frac{{b}^{6}}{{a}^{7} \left ( ax+b \right ) }}-6\,{\frac{{b}^{5}\ln \left ( ax+b \right ) }{{a}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(a+b/x)^2,x)
[Out]
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Maxima [A] time = 1.43714, size = 111, normalized size = 1.37 \[ -\frac{b^{6}}{a^{8} x + a^{7} b} - \frac{6 \, b^{5} \log \left (a x + b\right )}{a^{7}} + \frac{2 \, a^{4} x^{5} - 5 \, a^{3} b x^{4} + 10 \, a^{2} b^{2} x^{3} - 20 \, a b^{3} x^{2} + 50 \, b^{4} x}{10 \, a^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(a + b/x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21835, size = 130, normalized size = 1.6 \[ \frac{2 \, a^{6} x^{6} - 3 \, a^{5} b x^{5} + 5 \, a^{4} b^{2} x^{4} - 10 \, a^{3} b^{3} x^{3} + 30 \, a^{2} b^{4} x^{2} + 50 \, a b^{5} x - 10 \, b^{6} - 60 \,{\left (a b^{5} x + b^{6}\right )} \log \left (a x + b\right )}{10 \,{\left (a^{8} x + a^{7} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(a + b/x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.56412, size = 78, normalized size = 0.96 \[ - \frac{b^{6}}{a^{8} x + a^{7} b} + \frac{x^{5}}{5 a^{2}} - \frac{b x^{4}}{2 a^{3}} + \frac{b^{2} x^{3}}{a^{4}} - \frac{2 b^{3} x^{2}}{a^{5}} + \frac{5 b^{4} x}{a^{6}} - \frac{6 b^{5} \log{\left (a x + b \right )}}{a^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(a+b/x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.221983, size = 115, normalized size = 1.42 \[ -\frac{6 \, b^{5}{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{7}} - \frac{b^{6}}{{\left (a x + b\right )} a^{7}} + \frac{2 \, a^{8} x^{5} - 5 \, a^{7} b x^{4} + 10 \, a^{6} b^{2} x^{3} - 20 \, a^{5} b^{3} x^{2} + 50 \, a^{4} b^{4} x}{10 \, a^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(a + b/x)^2,x, algorithm="giac")
[Out]