Optimal. Leaf size=17 \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]
[Out]
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Rubi [A] time = 0.0136834, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]
Antiderivative was successfully verified.
[In] Int[x^8*(a + b*x^7),x]
[Out]
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Rubi in Sympy [A] time = 2.99811, size = 12, normalized size = 0.71 \[ \frac{a x^{9}}{9} + \frac{b x^{16}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8*(b*x**7+a),x)
[Out]
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Mathematica [A] time = 0.00188502, size = 17, normalized size = 1. \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]
Antiderivative was successfully verified.
[In] Integrate[x^8*(a + b*x^7),x]
[Out]
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Maple [A] time = 0., size = 14, normalized size = 0.8 \[{\frac{a{x}^{9}}{9}}+{\frac{b{x}^{16}}{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8*(b*x^7+a),x)
[Out]
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Maxima [A] time = 1.43871, size = 18, normalized size = 1.06 \[ \frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^7 + a)*x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.189639, size = 1, normalized size = 0.06 \[ \frac{1}{16} x^{16} b + \frac{1}{9} x^{9} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^7 + a)*x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.066645, size = 12, normalized size = 0.71 \[ \frac{a x^{9}}{9} + \frac{b x^{16}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8*(b*x**7+a),x)
[Out]
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GIAC/XCAS [A] time = 0.219435, size = 18, normalized size = 1.06 \[ \frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^7 + a)*x^8,x, algorithm="giac")
[Out]