Optimal. Leaf size=43 \[ -\frac{\log (a x+b)}{b^3}+\frac{1}{b^2 (a x+b)}+\frac{1}{2 b (a x+b)^2}+\frac{\log (x)}{b^3} \]
[Out]
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Rubi [A] time = 0.0645575, antiderivative size = 43, 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 \[ -\frac{\log (a x+b)}{b^3}+\frac{1}{b^2 (a x+b)}+\frac{1}{2 b (a x+b)^2}+\frac{\log (x)}{b^3} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^3*x^4),x]
[Out]
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Rubi in Sympy [A] time = 10.4382, size = 37, normalized size = 0.86 \[ \frac{1}{2 b \left (a x + b\right )^{2}} + \frac{1}{b^{2} \left (a x + b\right )} + \frac{\log{\left (x \right )}}{b^{3}} - \frac{\log{\left (a x + b \right )}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**3/x**4,x)
[Out]
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Mathematica [A] time = 0.0518987, size = 37, normalized size = 0.86 \[ \frac{\frac{b (2 a x+3 b)}{(a x+b)^2}-2 \log (a x+b)+2 \log (x)}{2 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^3*x^4),x]
[Out]
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Maple [A] time = 0.011, size = 42, normalized size = 1. \[{\frac{1}{2\,b \left ( ax+b \right ) ^{2}}}+{\frac{1}{{b}^{2} \left ( ax+b \right ) }}+{\frac{\ln \left ( x \right ) }{{b}^{3}}}-{\frac{\ln \left ( ax+b \right ) }{{b}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^3/x^4,x)
[Out]
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Maxima [A] time = 1.43333, size = 69, normalized size = 1.6 \[ \frac{2 \, a x + 3 \, b}{2 \,{\left (a^{2} b^{2} x^{2} + 2 \, a b^{3} x + b^{4}\right )}} - \frac{\log \left (a x + b\right )}{b^{3}} + \frac{\log \left (x\right )}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^3*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233208, size = 108, normalized size = 2.51 \[ \frac{2 \, a b x + 3 \, b^{2} - 2 \,{\left (a^{2} x^{2} + 2 \, a b x + b^{2}\right )} \log \left (a x + b\right ) + 2 \,{\left (a^{2} x^{2} + 2 \, a b x + b^{2}\right )} \log \left (x\right )}{2 \,{\left (a^{2} b^{3} x^{2} + 2 \, a b^{4} x + b^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^3*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.70518, size = 46, normalized size = 1.07 \[ \frac{2 a x + 3 b}{2 a^{2} b^{2} x^{2} + 4 a b^{3} x + 2 b^{4}} + \frac{\log{\left (x \right )} - \log{\left (x + \frac{b}{a} \right )}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**3/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.235995, size = 58, normalized size = 1.35 \[ -\frac{{\rm ln}\left ({\left | a x + b \right |}\right )}{b^{3}} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{b^{3}} + \frac{2 \, a b x + 3 \, b^{2}}{2 \,{\left (a x + b\right )}^{2} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^3*x^4),x, algorithm="giac")
[Out]