Optimal. Leaf size=43 \[ -\frac{a^3}{14 x^{14}}-\frac{a^2 b}{4 x^{12}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8} \]
[Out]
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Rubi [A] time = 0.0555315, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^3}{14 x^{14}}-\frac{a^2 b}{4 x^{12}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^15,x]
[Out]
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Rubi in Sympy [A] time = 9.21817, size = 39, normalized size = 0.91 \[ - \frac{a^{3}}{14 x^{14}} - \frac{a^{2} b}{4 x^{12}} - \frac{3 a b^{2}}{10 x^{10}} - \frac{b^{3}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**15,x)
[Out]
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Mathematica [A] time = 0.0120506, size = 43, normalized size = 1. \[ -\frac{a^3}{14 x^{14}}-\frac{a^2 b}{4 x^{12}}-\frac{3 a b^2}{10 x^{10}}-\frac{b^3}{8 x^8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^15,x]
[Out]
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Maple [A] time = 0.007, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{14\,{x}^{14}}}-{\frac{{a}^{2}b}{4\,{x}^{12}}}-{\frac{3\,a{b}^{2}}{10\,{x}^{10}}}-{\frac{{b}^{3}}{8\,{x}^{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^15,x)
[Out]
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Maxima [A] time = 1.34464, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^15,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193665, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^15,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.90044, size = 39, normalized size = 0.91 \[ - \frac{20 a^{3} + 70 a^{2} b x^{2} + 84 a b^{2} x^{4} + 35 b^{3} x^{6}}{280 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**15,x)
[Out]
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GIAC/XCAS [A] time = 0.21349, size = 50, normalized size = 1.16 \[ -\frac{35 \, b^{3} x^{6} + 84 \, a b^{2} x^{4} + 70 \, a^{2} b x^{2} + 20 \, a^{3}}{280 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^15,x, algorithm="giac")
[Out]