Optimal. Leaf size=30 \[ \frac{a^2 x^9}{9}+\frac{1}{8} a b x^{16}+\frac{b^2 x^{23}}{23} \]
[Out]
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Rubi [A] time = 0.0332043, antiderivative size = 30, 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 \[ \frac{a^2 x^9}{9}+\frac{1}{8} a b x^{16}+\frac{b^2 x^{23}}{23} \]
Antiderivative was successfully verified.
[In] Int[x^8*(a + b*x^7)^2,x]
[Out]
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Rubi in Sympy [A] time = 5.44697, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{9}}{9} + \frac{a b x^{16}}{8} + \frac{b^{2} x^{23}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8*(b*x**7+a)**2,x)
[Out]
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Mathematica [A] time = 0.0014604, size = 30, normalized size = 1. \[ \frac{a^2 x^9}{9}+\frac{1}{8} a b x^{16}+\frac{b^2 x^{23}}{23} \]
Antiderivative was successfully verified.
[In] Integrate[x^8*(a + b*x^7)^2,x]
[Out]
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{a}^{2}{x}^{9}}{9}}+{\frac{ab{x}^{16}}{8}}+{\frac{{b}^{2}{x}^{23}}{23}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8*(b*x^7+a)^2,x)
[Out]
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Maxima [A] time = 1.43824, size = 32, normalized size = 1.07 \[ \frac{1}{23} \, b^{2} x^{23} + \frac{1}{8} \, a b x^{16} + \frac{1}{9} \, a^{2} x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^7 + a)^2*x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.190358, size = 1, normalized size = 0.03 \[ \frac{1}{23} x^{23} b^{2} + \frac{1}{8} x^{16} b a + \frac{1}{9} x^{9} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^7 + a)^2*x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.093494, size = 24, normalized size = 0.8 \[ \frac{a^{2} x^{9}}{9} + \frac{a b x^{16}}{8} + \frac{b^{2} x^{23}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8*(b*x**7+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217949, size = 32, normalized size = 1.07 \[ \frac{1}{23} \, b^{2} x^{23} + \frac{1}{8} \, a b x^{16} + \frac{1}{9} \, a^{2} x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^7 + a)^2*x^8,x, algorithm="giac")
[Out]