Optimal. Leaf size=18 \[ \frac{x}{a}-\frac{b \log (a x+b)}{a^2} \]
[Out]
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Rubi [A] time = 0.0309238, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{x}{a}-\frac{b \log (a x+b)}{a^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^(-1),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{a}\, dx - \frac{b \log{\left (a x + b \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x),x)
[Out]
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Mathematica [A] time = 0.00440873, size = 18, normalized size = 1. \[ \frac{x}{a}-\frac{b \log (a x+b)}{a^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^(-1),x]
[Out]
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Maple [A] time = 0.003, size = 19, normalized size = 1.1 \[{\frac{x}{a}}-{\frac{b\ln \left ( ax+b \right ) }{{a}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x),x)
[Out]
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Maxima [A] time = 1.44092, size = 24, normalized size = 1.33 \[ \frac{x}{a} - \frac{b \log \left (a x + b\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a + b/x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218557, size = 23, normalized size = 1.28 \[ \frac{a x - b \log \left (a x + b\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a + b/x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.04563, size = 14, normalized size = 0.78 \[ \frac{x}{a} - \frac{b \log{\left (a x + b \right )}}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x),x)
[Out]
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GIAC/XCAS [A] time = 0.225533, size = 26, normalized size = 1.44 \[ \frac{x}{a} - \frac{b{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a + b/x),x, algorithm="giac")
[Out]