Optimal. Leaf size=30 \[ \frac{(a x+b)^5}{5 a^2}-\frac{b (a x+b)^4}{4 a^2} \]
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Rubi [A] time = 0.0391365, antiderivative size = 30, 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 \[ \frac{(a x+b)^5}{5 a^2}-\frac{b (a x+b)^4}{4 a^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3*x^4,x]
[Out]
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Rubi in Sympy [A] time = 7.65092, size = 24, normalized size = 0.8 \[ - \frac{b \left (a x + b\right )^{4}}{4 a^{2}} + \frac{\left (a x + b\right )^{5}}{5 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3*x**4,x)
[Out]
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Mathematica [A] time = 0.00262162, size = 40, normalized size = 1.33 \[ \frac{a^3 x^5}{5}+\frac{3}{4} a^2 b x^4+a b^2 x^3+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3*x^4,x]
[Out]
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Maple [A] time = 0.001, size = 35, normalized size = 1.2 \[{\frac{{a}^{3}{x}^{5}}{5}}+{\frac{3\,{a}^{2}b{x}^{4}}{4}}+a{b}^{2}{x}^{3}+{\frac{{b}^{3}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3*x^4,x)
[Out]
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Maxima [A] time = 1.44378, size = 46, normalized size = 1.53 \[ \frac{1}{5} \, a^{3} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + a b^{2} x^{3} + \frac{1}{2} \, b^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209575, size = 46, normalized size = 1.53 \[ \frac{1}{5} \, a^{3} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + a b^{2} x^{3} + \frac{1}{2} \, b^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.091865, size = 36, normalized size = 1.2 \[ \frac{a^{3} x^{5}}{5} + \frac{3 a^{2} b x^{4}}{4} + a b^{2} x^{3} + \frac{b^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3*x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.223652, size = 46, normalized size = 1.53 \[ \frac{1}{5} \, a^{3} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + a b^{2} x^{3} + \frac{1}{2} \, b^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3*x^4,x, algorithm="giac")
[Out]