Optimal. Leaf size=40 \[ \frac{b \left (a+b x^2\right )^4}{40 a^2 x^8}-\frac{\left (a+b x^2\right )^4}{10 a x^{10}} \]
[Out]
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Rubi [A] time = 0.0563301, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{b \left (a+b x^2\right )^4}{40 a^2 x^8}-\frac{\left (a+b x^2\right )^4}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^11,x]
[Out]
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Rubi in Sympy [A] time = 9.3241, size = 39, normalized size = 0.98 \[ - \frac{a^{3}}{10 x^{10}} - \frac{3 a^{2} b}{8 x^{8}} - \frac{a b^{2}}{2 x^{6}} - \frac{b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**11,x)
[Out]
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Mathematica [A] time = 0.00714586, size = 43, normalized size = 1.08 \[ -\frac{a^3}{10 x^{10}}-\frac{3 a^2 b}{8 x^8}-\frac{a b^2}{2 x^6}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^11,x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 0.9 \[ -{\frac{{a}^{3}}{10\,{x}^{10}}}-{\frac{a{b}^{2}}{2\,{x}^{6}}}-{\frac{{b}^{3}}{4\,{x}^{4}}}-{\frac{3\,{a}^{2}b}{8\,{x}^{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^11,x)
[Out]
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Maxima [A] time = 1.34767, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{6} + 20 \, a b^{2} x^{4} + 15 \, a^{2} b x^{2} + 4 \, a^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193905, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{6} + 20 \, a b^{2} x^{4} + 15 \, a^{2} b x^{2} + 4 \, a^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.70705, size = 39, normalized size = 0.98 \[ - \frac{4 a^{3} + 15 a^{2} b x^{2} + 20 a b^{2} x^{4} + 10 b^{3} x^{6}}{40 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.20664, size = 50, normalized size = 1.25 \[ -\frac{10 \, b^{3} x^{6} + 20 \, a b^{2} x^{4} + 15 \, a^{2} b x^{2} + 4 \, a^{3}}{40 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^11,x, algorithm="giac")
[Out]