Optimal. Leaf size=43 \[ \frac{a^3 x^8}{8}+\frac{3}{10} a^2 b x^{10}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{14}}{14} \]
[Out]
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Rubi [A] time = 0.0782016, 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 \[ \frac{a^3 x^8}{8}+\frac{3}{10} a^2 b x^{10}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{14}}{14} \]
Antiderivative was successfully verified.
[In] Int[x^7*(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 10.4321, size = 37, normalized size = 0.86 \[ \frac{a^{3} x^{8}}{8} + \frac{3 a^{2} b x^{10}}{10} + \frac{a b^{2} x^{12}}{4} + \frac{b^{3} x^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7*(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.00327151, size = 43, normalized size = 1. \[ \frac{a^3 x^8}{8}+\frac{3}{10} a^2 b x^{10}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{14}}{14} \]
Antiderivative was successfully verified.
[In] Integrate[x^7*(a + b*x^2)^3,x]
[Out]
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Maple [A] time = 0., size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{8}}{8}}+{\frac{3\,{a}^{2}b{x}^{10}}{10}}+{\frac{a{b}^{2}{x}^{12}}{4}}+{\frac{{b}^{3}{x}^{14}}{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7*(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.34176, size = 47, normalized size = 1.09 \[ \frac{1}{14} \, b^{3} x^{14} + \frac{1}{4} \, a b^{2} x^{12} + \frac{3}{10} \, a^{2} b x^{10} + \frac{1}{8} \, a^{3} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182858, size = 1, normalized size = 0.02 \[ \frac{1}{14} x^{14} b^{3} + \frac{1}{4} x^{12} b^{2} a + \frac{3}{10} x^{10} b a^{2} + \frac{1}{8} x^{8} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.105183, size = 37, normalized size = 0.86 \[ \frac{a^{3} x^{8}}{8} + \frac{3 a^{2} b x^{10}}{10} + \frac{a b^{2} x^{12}}{4} + \frac{b^{3} x^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7*(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.205491, size = 47, normalized size = 1.09 \[ \frac{1}{14} \, b^{3} x^{14} + \frac{1}{4} \, a b^{2} x^{12} + \frac{3}{10} \, a^{2} b x^{10} + \frac{1}{8} \, a^{3} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^7,x, algorithm="giac")
[Out]