Optimal. Leaf size=17 \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]
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Rubi [A] time = 0.0049247, 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, Rules used = {14} \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x^8 \left (a+b x^7\right ) \, dx &=\int \left (a x^8+b x^{15}\right ) \, dx\\ &=\frac{a x^9}{9}+\frac{b x^{16}}{16}\\ \end{align*}
Mathematica [A] time = 0.0011724, size = 17, normalized size = 1. \[ \frac{a x^9}{9}+\frac{b x^{16}}{16} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.8 \begin{align*}{\frac{a{x}^{9}}{9}}+{\frac{b{x}^{16}}{16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949015, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47321, size = 34, normalized size = 2. \begin{align*} \frac{1}{16} x^{16} b + \frac{1}{9} x^{9} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.052927, size = 12, normalized size = 0.71 \begin{align*} \frac{a x^{9}}{9} + \frac{b x^{16}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10248, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{16} \, b x^{16} + \frac{1}{9} \, a x^{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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