Optimal. Leaf size=23 \[ \frac{b}{a^2 (a x+b)}+\frac{\log (a x+b)}{a^2} \]
[Out]
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Rubi [A] time = 0.0433145, antiderivative size = 23, 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 \[ \frac{b}{a^2 (a x+b)}+\frac{\log (a x+b)}{a^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^2*x),x]
[Out]
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Rubi in Sympy [A] time = 7.56412, size = 19, normalized size = 0.83 \[ \frac{b}{a^{2} \left (a x + b\right )} + \frac{\log{\left (a x + b \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**2/x,x)
[Out]
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Mathematica [A] time = 0.0125417, size = 20, normalized size = 0.87 \[ \frac{\frac{b}{a x+b}+\log (a x+b)}{a^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^2*x),x]
[Out]
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Maple [A] time = 0.007, size = 24, normalized size = 1. \[{\frac{b}{{a}^{2} \left ( ax+b \right ) }}+{\frac{\ln \left ( ax+b \right ) }{{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^2/x,x)
[Out]
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Maxima [A] time = 1.45658, size = 35, normalized size = 1.52 \[ \frac{b}{a^{3} x + a^{2} b} + \frac{\log \left (a x + b\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219615, size = 38, normalized size = 1.65 \[ \frac{{\left (a x + b\right )} \log \left (a x + b\right ) + b}{a^{3} x + a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.16313, size = 20, normalized size = 0.87 \[ \frac{b}{a^{3} x + a^{2} b} + \frac{\log{\left (a x + b \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**2/x,x)
[Out]
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GIAC/XCAS [A] time = 0.223905, size = 32, normalized size = 1.39 \[ \frac{{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{2}} + \frac{b}{{\left (a x + b\right )} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^2*x),x, algorithm="giac")
[Out]