Optimal. Leaf size=16 \[ \frac {\left (a+b x^2\right )^9}{18 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {261} \[ \frac {\left (a+b x^2\right )^9}{18 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \left (a+b x^2\right )^8 \, dx &=\frac {\left (a+b x^2\right )^9}{18 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {\left (a+b x^2\right )^9}{18 b} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 90, normalized size = 5.62 \[ \frac {1}{18} x^{18} b^{8} + \frac {1}{2} x^{16} b^{7} a + 2 x^{14} b^{6} a^{2} + \frac {14}{3} x^{12} b^{5} a^{3} + 7 x^{10} b^{4} a^{4} + 7 x^{8} b^{3} a^{5} + \frac {14}{3} x^{6} b^{2} a^{6} + 2 x^{4} b a^{7} + \frac {1}{2} x^{2} a^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{2} + a\right )}^{9}}{18 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 91, normalized size = 5.69 \[ \frac {1}{18} b^{8} x^{18}+\frac {1}{2} a \,b^{7} x^{16}+2 a^{2} b^{6} x^{14}+\frac {14}{3} a^{3} b^{5} x^{12}+7 a^{4} b^{4} x^{10}+7 a^{5} b^{3} x^{8}+\frac {14}{3} a^{6} b^{2} x^{6}+2 a^{7} b \,x^{4}+\frac {1}{2} a^{8} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{2} + a\right )}^{9}}{18 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.61, size = 14, normalized size = 0.88 \[ \frac {{\left (b\,x^2+a\right )}^9}{18\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 99, normalized size = 6.19 \[ \frac {a^{8} x^{2}}{2} + 2 a^{7} b x^{4} + \frac {14 a^{6} b^{2} x^{6}}{3} + 7 a^{5} b^{3} x^{8} + 7 a^{4} b^{4} x^{10} + \frac {14 a^{3} b^{5} x^{12}}{3} + 2 a^{2} b^{6} x^{14} + \frac {a b^{7} x^{16}}{2} + \frac {b^{8} x^{18}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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