Optimal. Leaf size=41 \[ -\frac{a^3}{7 x^7}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2} \]
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Rubi [A] time = 0.0374444, antiderivative size = 41, 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 \[ -\frac{a^3}{7 x^7}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^8,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{3}}{7 x^{7}} - \frac{3 a^{2} b}{4 x^{4}} - \frac{3 a b^{2}}{x} + b^{3} \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**8,x)
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Mathematica [A] time = 0.0072041, size = 41, normalized size = 1. \[ -\frac{a^3}{7 x^7}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{x}+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^8,x]
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Maple [A] time = 0.008, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{3}}{7\,{x}^{7}}}-{\frac{3\,{a}^{2}b}{4\,{x}^{4}}}-3\,{\frac{a{b}^{2}}{x}}+{\frac{{b}^{3}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^8,x)
[Out]
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Maxima [A] time = 1.41785, size = 51, normalized size = 1.24 \[ \frac{1}{2} \, b^{3} x^{2} - \frac{84 \, a b^{2} x^{6} + 21 \, a^{2} b x^{3} + 4 \, a^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202771, size = 50, normalized size = 1.22 \[ \frac{14 \, b^{3} x^{9} - 84 \, a b^{2} x^{6} - 21 \, a^{2} b x^{3} - 4 \, a^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.46135, size = 37, normalized size = 0.9 \[ \frac{b^{3} x^{2}}{2} - \frac{4 a^{3} + 21 a^{2} b x^{3} + 84 a b^{2} x^{6}}{28 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.222172, size = 51, normalized size = 1.24 \[ \frac{1}{2} \, b^{3} x^{2} - \frac{84 \, a b^{2} x^{6} + 21 \, a^{2} b x^{3} + 4 \, a^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^8,x, algorithm="giac")
[Out]