Optimal. Leaf size=29 \[ -\frac{\log (a x+b)}{b^2}+\frac{1}{b (a x+b)}+\frac{\log (x)}{b^2} \]
[Out]
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Rubi [A] time = 0.0510818, antiderivative size = 29, 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 \[ -\frac{\log (a x+b)}{b^2}+\frac{1}{b (a x+b)}+\frac{\log (x)}{b^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^2*x^3),x]
[Out]
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Rubi in Sympy [A] time = 7.83518, size = 24, normalized size = 0.83 \[ \frac{1}{b \left (a x + b\right )} + \frac{\log{\left (x \right )}}{b^{2}} - \frac{\log{\left (a x + b \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**2/x**3,x)
[Out]
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Mathematica [A] time = 0.0165118, size = 24, normalized size = 0.83 \[ \frac{\frac{b}{a x+b}-\log (a x+b)+\log (x)}{b^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^2*x^3),x]
[Out]
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Maple [A] time = 0.012, size = 30, normalized size = 1. \[{\frac{1}{b \left ( ax+b \right ) }}+{\frac{\ln \left ( x \right ) }{{b}^{2}}}-{\frac{\ln \left ( ax+b \right ) }{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^2/x^3,x)
[Out]
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Maxima [A] time = 1.4555, size = 38, normalized size = 1.31 \[ \frac{1}{a b x + b^{2}} - \frac{\log \left (a x + b\right )}{b^{2}} + \frac{\log \left (x\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225335, size = 53, normalized size = 1.83 \[ -\frac{{\left (a x + b\right )} \log \left (a x + b\right ) -{\left (a x + b\right )} \log \left (x\right ) - b}{a b^{2} x + b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.40899, size = 22, normalized size = 0.76 \[ \frac{1}{a b x + b^{2}} + \frac{\log{\left (x \right )} - \log{\left (x + \frac{b}{a} \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**2/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.232606, size = 42, normalized size = 1.45 \[ -\frac{{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{2}} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{b^{2}} + \frac{1}{{\left (a x + b\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x^3),x, algorithm="giac")
[Out]