Optimal. Leaf size=33 \[ a^3 x+3 a^2 b \log (x)-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2} \]
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Rubi [A] time = 0.0366301, antiderivative size = 33, 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 \[ a^3 x+3 a^2 b \log (x)-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 3 a^{2} b \log{\left (x \right )} - \frac{3 a b^{2}}{x} - \frac{b^{3}}{2 x^{2}} + \int a^{3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3,x)
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Mathematica [A] time = 0.00624543, size = 33, normalized size = 1. \[ a^3 x+3 a^2 b \log (x)-\frac{3 a b^2}{x}-\frac{b^3}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3,x]
[Out]
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Maple [A] time = 0.009, size = 32, normalized size = 1. \[ -{\frac{{b}^{3}}{2\,{x}^{2}}}-3\,{\frac{a{b}^{2}}{x}}+{a}^{3}x+3\,{a}^{2}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3,x)
[Out]
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Maxima [A] time = 1.43691, size = 42, normalized size = 1.27 \[ a^{3} x + 3 \, a^{2} b \log \left (x\right ) - \frac{3 \, a b^{2}}{x} - \frac{b^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218149, size = 50, normalized size = 1.52 \[ \frac{2 \, a^{3} x^{3} + 6 \, a^{2} b x^{2} \log \left (x\right ) - 6 \, a b^{2} x - b^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.29378, size = 31, normalized size = 0.94 \[ a^{3} x + 3 a^{2} b \log{\left (x \right )} - \frac{6 a b^{2} x + b^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.219682, size = 42, normalized size = 1.27 \[ a^{3} x + 3 \, a^{2} b{\rm ln}\left ({\left | x \right |}\right ) - \frac{6 \, a b^{2} x + b^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3,x, algorithm="giac")
[Out]