Optimal. Leaf size=36 \[ \frac{a (a x+b)^4}{20 b^2 x^4}-\frac{(a x+b)^4}{5 b x^5} \]
[Out]
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Rubi [A] time = 0.0366419, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{a (a x+b)^4}{20 b^2 x^4}-\frac{(a x+b)^4}{5 b x^5} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x^3,x]
[Out]
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Rubi in Sympy [A] time = 7.83464, size = 37, normalized size = 1.03 \[ - \frac{a^{3}}{2 x^{2}} - \frac{a^{2} b}{x^{3}} - \frac{3 a b^{2}}{4 x^{4}} - \frac{b^{3}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x**3,x)
[Out]
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Mathematica [A] time = 0.00989323, size = 41, normalized size = 1.14 \[ -\frac{a^3}{2 x^2}-\frac{a^2 b}{x^3}-\frac{3 a b^2}{4 x^4}-\frac{b^3}{5 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x^3,x]
[Out]
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Maple [A] time = 0.007, size = 36, normalized size = 1. \[ -{\frac{3\,a{b}^{2}}{4\,{x}^{4}}}-{\frac{{a}^{2}b}{{x}^{3}}}-{\frac{{a}^{3}}{2\,{x}^{2}}}-{\frac{{b}^{3}}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x^3,x)
[Out]
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Maxima [A] time = 1.44363, size = 47, normalized size = 1.31 \[ -\frac{10 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x + 4 \, b^{3}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211327, size = 47, normalized size = 1.31 \[ -\frac{10 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x + 4 \, b^{3}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.46644, size = 37, normalized size = 1.03 \[ - \frac{10 a^{3} x^{3} + 20 a^{2} b x^{2} + 15 a b^{2} x + 4 b^{3}}{20 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.222589, size = 47, normalized size = 1.31 \[ -\frac{10 \, a^{3} x^{3} + 20 \, a^{2} b x^{2} + 15 \, a b^{2} x + 4 \, b^{3}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^3,x, algorithm="giac")
[Out]