Optimal. Leaf size=11 \[ \frac {1}{18} \left (x^2+5\right )^9 \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {261} \[ \frac {1}{18} \left (x^2+5\right )^9 \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \left (5+x^2\right )^8 \, dx &=\frac {1}{18} \left (5+x^2\right )^9\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \frac {1}{18} \left (x^2+5\right )^9 \]
Antiderivative was successfully verified.
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fricas [B] time = 0.34, size = 46, normalized size = 4.18 \[ \frac {1}{18} x^{18} + \frac {5}{2} x^{16} + 50 x^{14} + \frac {1750}{3} x^{12} + 4375 x^{10} + 21875 x^{8} + \frac {218750}{3} x^{6} + 156250 x^{4} + \frac {390625}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 9, normalized size = 0.82 \[ \frac {1}{18} \, {\left (x^{2} + 5\right )}^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 47, normalized size = 4.27 \[ \frac {1}{18} x^{18}+\frac {5}{2} x^{16}+50 x^{14}+\frac {1750}{3} x^{12}+4375 x^{10}+21875 x^{8}+\frac {218750}{3} x^{6}+156250 x^{4}+\frac {390625}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 9, normalized size = 0.82 \[ \frac {1}{18} \, {\left (x^{2} + 5\right )}^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 9, normalized size = 0.82 \[ \frac {{\left (x^2+5\right )}^9}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.06, size = 51, normalized size = 4.64 \[ \frac {x^{18}}{18} + \frac {5 x^{16}}{2} + 50 x^{14} + \frac {1750 x^{12}}{3} + 4375 x^{10} + 21875 x^{8} + \frac {218750 x^{6}}{3} + 156250 x^{4} + \frac {390625 x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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