Optimal. Leaf size=61 \[ -\frac{a^5}{8 x^8}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7} \]
[Out]
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Rubi [A] time = 0.0602035, antiderivative size = 61, 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 \[ -\frac{a^5}{8 x^8}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^5/x^9,x]
[Out]
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Rubi in Sympy [A] time = 11.0784, size = 58, normalized size = 0.95 \[ - \frac{a^{5}}{8 x^{8}} - \frac{a^{4} b}{x^{5}} - \frac{5 a^{3} b^{2}}{x^{2}} + 10 a^{2} b^{3} x + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5/x**9,x)
[Out]
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Mathematica [A] time = 0.00747608, size = 61, normalized size = 1. \[ -\frac{a^5}{8 x^8}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{x^2}+10 a^2 b^3 x+\frac{5}{4} a b^4 x^4+\frac{b^5 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^5/x^9,x]
[Out]
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Maple [A] time = 0.008, size = 56, normalized size = 0.9 \[ -{\frac{{a}^{5}}{8\,{x}^{8}}}-{\frac{{a}^{4}b}{{x}^{5}}}-5\,{\frac{{a}^{3}{b}^{2}}{{x}^{2}}}+10\,{a}^{2}{b}^{3}x+{\frac{5\,a{b}^{4}{x}^{4}}{4}}+{\frac{{b}^{5}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5/x^9,x)
[Out]
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Maxima [A] time = 1.4396, size = 76, normalized size = 1.25 \[ \frac{1}{7} \, b^{5} x^{7} + \frac{5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac{40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205113, size = 80, normalized size = 1.31 \[ \frac{8 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 560 \, a^{2} b^{3} x^{9} - 280 \, a^{3} b^{2} x^{6} - 56 \, a^{4} b x^{3} - 7 \, a^{5}}{56 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.61977, size = 60, normalized size = 0.98 \[ 10 a^{2} b^{3} x + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{7}}{7} - \frac{a^{5} + 8 a^{4} b x^{3} + 40 a^{3} b^{2} x^{6}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.21905, size = 76, normalized size = 1.25 \[ \frac{1}{7} \, b^{5} x^{7} + \frac{5}{4} \, a b^{4} x^{4} + 10 \, a^{2} b^{3} x - \frac{40 \, a^{3} b^{2} x^{6} + 8 \, a^{4} b x^{3} + a^{5}}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5/x^9,x, algorithm="giac")
[Out]