Optimal. Leaf size=39 \[ -\frac{a^3}{7 x^7}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{x^3}-\frac{b^3}{x} \]
[Out]
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Rubi [A] time = 0.0418237, antiderivative size = 39, 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 \[ -\frac{a^3}{7 x^7}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{x^3}-\frac{b^3}{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^8,x]
[Out]
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Rubi in Sympy [A] time = 7.57277, size = 34, normalized size = 0.87 \[ - \frac{a^{3}}{7 x^{7}} - \frac{3 a^{2} b}{5 x^{5}} - \frac{a b^{2}}{x^{3}} - \frac{b^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**8,x)
[Out]
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Mathematica [A] time = 0.00694587, size = 39, normalized size = 1. \[ -\frac{a^3}{7 x^7}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{x^3}-\frac{b^3}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^8,x]
[Out]
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Maple [A] time = 0.007, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{3}}{7\,{x}^{7}}}-{\frac{3\,{a}^{2}b}{5\,{x}^{5}}}-{\frac{a{b}^{2}}{{x}^{3}}}-{\frac{{b}^{3}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^8,x)
[Out]
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Maxima [A] time = 1.34556, size = 50, normalized size = 1.28 \[ -\frac{35 \, b^{3} x^{6} + 35 \, a b^{2} x^{4} + 21 \, a^{2} b x^{2} + 5 \, a^{3}}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220698, size = 50, normalized size = 1.28 \[ -\frac{35 \, b^{3} x^{6} + 35 \, a b^{2} x^{4} + 21 \, a^{2} b x^{2} + 5 \, a^{3}}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.54212, size = 39, normalized size = 1. \[ - \frac{5 a^{3} + 21 a^{2} b x^{2} + 35 a b^{2} x^{4} + 35 b^{3} x^{6}}{35 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.206679, size = 50, normalized size = 1.28 \[ -\frac{35 \, b^{3} x^{6} + 35 \, a b^{2} x^{4} + 21 \, a^{2} b x^{2} + 5 \, a^{3}}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^8,x, algorithm="giac")
[Out]