Optimal. Leaf size=43 \[ -\frac{a^3}{2 x^2}+\frac{3}{2} a^2 b x^2+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10} \]
[Out]
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Rubi [A] time = 0.037318, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^3}{2 x^2}+\frac{3}{2} a^2 b x^2+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^3/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{2 x^{2}} + 3 a^{2} b \int x\, dx + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**3/x**3,x)
[Out]
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Mathematica [A] time = 0.01141, size = 43, normalized size = 1. \[ -\frac{a^3}{2 x^2}+\frac{3}{2} a^2 b x^2+\frac{1}{2} a b^2 x^6+\frac{b^3 x^{10}}{10} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^3/x^3,x]
[Out]
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Maple [A] time = 0.004, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{2\,{x}^{2}}}+{\frac{3\,{a}^{2}b{x}^{2}}{2}}+{\frac{a{b}^{2}{x}^{6}}{2}}+{\frac{{b}^{3}{x}^{10}}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^3/x^3,x)
[Out]
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Maxima [A] time = 1.44137, size = 47, normalized size = 1.09 \[ \frac{1}{10} \, b^{3} x^{10} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{2} \, a^{2} b x^{2} - \frac{a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216383, size = 49, normalized size = 1.14 \[ \frac{b^{3} x^{12} + 5 \, a b^{2} x^{8} + 15 \, a^{2} b x^{4} - 5 \, a^{3}}{10 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.07261, size = 37, normalized size = 0.86 \[ - \frac{a^{3}}{2 x^{2}} + \frac{3 a^{2} b x^{2}}{2} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.21524, size = 47, normalized size = 1.09 \[ \frac{1}{10} \, b^{3} x^{10} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{2} \, a^{2} b x^{2} - \frac{a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3/x^3,x, algorithm="giac")
[Out]