Optimal. Leaf size=28 \[ -\frac{a \log (x)}{b^2}+\frac{a \log (a x+b)}{b^2}-\frac{1}{b x} \]
[Out]
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Rubi [A] time = 0.046779, antiderivative size = 28, 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 \[ -\frac{a \log (x)}{b^2}+\frac{a \log (a x+b)}{b^2}-\frac{1}{b x} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)*x^3),x]
[Out]
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Rubi in Sympy [A] time = 7.22525, size = 24, normalized size = 0.86 \[ - \frac{a \log{\left (x \right )}}{b^{2}} + \frac{a \log{\left (a x + b \right )}}{b^{2}} - \frac{1}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)/x**3,x)
[Out]
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Mathematica [A] time = 0.00746488, size = 28, normalized size = 1. \[ -\frac{a \log (x)}{b^2}+\frac{a \log (a x+b)}{b^2}-\frac{1}{b x} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)*x^3),x]
[Out]
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Maple [A] time = 0.012, size = 29, normalized size = 1. \[ -{\frac{1}{bx}}-{\frac{a\ln \left ( x \right ) }{{b}^{2}}}+{\frac{a\ln \left ( ax+b \right ) }{{b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)/x^3,x)
[Out]
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Maxima [A] time = 1.43579, size = 38, normalized size = 1.36 \[ \frac{a \log \left (a x + b\right )}{b^{2}} - \frac{a \log \left (x\right )}{b^{2}} - \frac{1}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227891, size = 35, normalized size = 1.25 \[ \frac{a x \log \left (a x + b\right ) - a x \log \left (x\right ) - b}{b^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.28784, size = 19, normalized size = 0.68 \[ \frac{a \left (- \log{\left (x \right )} + \log{\left (x + \frac{b}{a} \right )}\right )}{b^{2}} - \frac{1}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.223476, size = 41, normalized size = 1.46 \[ \frac{a{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{2}} - \frac{a{\rm ln}\left ({\left | x \right |}\right )}{b^{2}} - \frac{1}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x^3),x, algorithm="giac")
[Out]