Optimal. Leaf size=41 \[ -\frac{b^2}{2 a^3 (a x+b)^2}+\frac{2 b}{a^3 (a x+b)}+\frac{\log (a x+b)}{a^3} \]
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Rubi [A] time = 0.0636248, antiderivative size = 41, 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 \[ -\frac{b^2}{2 a^3 (a x+b)^2}+\frac{2 b}{a^3 (a x+b)}+\frac{\log (a x+b)}{a^3} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^3*x),x]
[Out]
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Rubi in Sympy [A] time = 11.0221, size = 36, normalized size = 0.88 \[ - \frac{b^{2}}{2 a^{3} \left (a x + b\right )^{2}} + \frac{2 b}{a^{3} \left (a x + b\right )} + \frac{\log{\left (a x + b \right )}}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**3/x,x)
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Mathematica [A] time = 0.0243065, size = 33, normalized size = 0.8 \[ \frac{\frac{b (4 a x+3 b)}{(a x+b)^2}+2 \log (a x+b)}{2 a^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^3*x),x]
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Maple [A] time = 0.009, size = 40, normalized size = 1. \[ -{\frac{{b}^{2}}{2\,{a}^{3} \left ( ax+b \right ) ^{2}}}+2\,{\frac{b}{{a}^{3} \left ( ax+b \right ) }}+{\frac{\ln \left ( ax+b \right ) }{{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^3/x,x)
[Out]
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Maxima [A] time = 1.42349, size = 65, normalized size = 1.59 \[ \frac{4 \, a b x + 3 \, b^{2}}{2 \,{\left (a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right )}} + \frac{\log \left (a x + b\right )}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^3*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223915, size = 82, normalized size = 2. \[ \frac{4 \, a b x + 3 \, b^{2} + 2 \,{\left (a^{2} x^{2} + 2 \, a b x + b^{2}\right )} \log \left (a x + b\right )}{2 \,{\left (a^{5} x^{2} + 2 \, a^{4} b x + a^{3} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^3*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.39151, size = 46, normalized size = 1.12 \[ \frac{4 a b x + 3 b^{2}}{2 a^{5} x^{2} + 4 a^{4} b x + 2 a^{3} b^{2}} + \frac{\log{\left (a x + b \right )}}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**3/x,x)
[Out]
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GIAC/XCAS [A] time = 0.224712, size = 50, normalized size = 1.22 \[ \frac{{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{3}} + \frac{4 \, b x + \frac{3 \, b^{2}}{a}}{2 \,{\left (a x + b\right )}^{2} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^3*x),x, algorithm="giac")
[Out]