Optimal. Leaf size=43 \[ -\frac{a^3}{11 x^{11}}-\frac{a^2 b}{3 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{5 x^5} \]
[Out]
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Rubi [A] time = 0.0412004, 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 \[ -\frac{a^3}{11 x^{11}}-\frac{a^2 b}{3 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{5 x^5} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^12,x]
[Out]
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Rubi in Sympy [A] time = 7.72359, size = 39, normalized size = 0.91 \[ - \frac{a^{3}}{11 x^{11}} - \frac{a^{2} b}{3 x^{9}} - \frac{3 a b^{2}}{7 x^{7}} - \frac{b^{3}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**12,x)
[Out]
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Mathematica [A] time = 0.011793, size = 43, normalized size = 1. \[ -\frac{a^3}{11 x^{11}}-\frac{a^2 b}{3 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{5 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^12,x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{11\,{x}^{11}}}-{\frac{{a}^{2}b}{3\,{x}^{9}}}-{\frac{3\,a{b}^{2}}{7\,{x}^{7}}}-{\frac{{b}^{3}}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^12,x)
[Out]
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Maxima [A] time = 1.34607, size = 50, normalized size = 1.16 \[ -\frac{231 \, b^{3} x^{6} + 495 \, a b^{2} x^{4} + 385 \, a^{2} b x^{2} + 105 \, a^{3}}{1155 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^12,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217779, size = 50, normalized size = 1.16 \[ -\frac{231 \, b^{3} x^{6} + 495 \, a b^{2} x^{4} + 385 \, a^{2} b x^{2} + 105 \, a^{3}}{1155 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^12,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.73748, size = 39, normalized size = 0.91 \[ - \frac{105 a^{3} + 385 a^{2} b x^{2} + 495 a b^{2} x^{4} + 231 b^{3} x^{6}}{1155 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**12,x)
[Out]
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GIAC/XCAS [A] time = 0.206268, size = 50, normalized size = 1.16 \[ -\frac{231 \, b^{3} x^{6} + 495 \, a b^{2} x^{4} + 385 \, a^{2} b x^{2} + 105 \, a^{3}}{1155 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^12,x, algorithm="giac")
[Out]