Optimal. Leaf size=16 \[ \frac {\left (a+b x^3\right )^9}{27 b} \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ \frac {\left (a+b x^3\right )^9}{27 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^2 \left (a+b x^3\right )^8 \, dx &=\frac {\left (a+b x^3\right )^9}{27 b}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 108, normalized size = 6.75 \[ \frac {a^8 x^3}{3}+\frac {4}{3} a^7 b x^6+\frac {28}{9} a^6 b^2 x^9+\frac {14}{3} a^5 b^3 x^{12}+\frac {14}{3} a^4 b^4 x^{15}+\frac {28}{9} a^3 b^5 x^{18}+\frac {4}{3} a^2 b^6 x^{21}+\frac {1}{3} a b^7 x^{24}+\frac {b^8 x^{27}}{27} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 90, normalized size = 5.62 \[ \frac {1}{27} x^{27} b^{8} + \frac {1}{3} x^{24} b^{7} a + \frac {4}{3} x^{21} b^{6} a^{2} + \frac {28}{9} x^{18} b^{5} a^{3} + \frac {14}{3} x^{15} b^{4} a^{4} + \frac {14}{3} x^{12} b^{3} a^{5} + \frac {28}{9} x^{9} b^{2} a^{6} + \frac {4}{3} x^{6} b a^{7} + \frac {1}{3} x^{3} a^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{3} + a\right )}^{9}}{27 \, b} \]
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 \[ \frac {1}{27} b^{8} x^{27}+\frac {1}{3} a \,b^{7} x^{24}+\frac {4}{3} a^{2} b^{6} x^{21}+\frac {28}{9} a^{3} b^{5} x^{18}+\frac {14}{3} a^{4} b^{4} x^{15}+\frac {14}{3} a^{5} b^{3} x^{12}+\frac {28}{9} a^{6} b^{2} x^{9}+\frac {4}{3} a^{7} b \,x^{6}+\frac {1}{3} a^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{3} + a\right )}^{9}}{27 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 14, normalized size = 0.88 \[ \frac {{\left (b\,x^3+a\right )}^9}{27\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 105, normalized size = 6.56 \[ \frac {a^{8} x^{3}}{3} + \frac {4 a^{7} b x^{6}}{3} + \frac {28 a^{6} b^{2} x^{9}}{9} + \frac {14 a^{5} b^{3} x^{12}}{3} + \frac {14 a^{4} b^{4} x^{15}}{3} + \frac {28 a^{3} b^{5} x^{18}}{9} + \frac {4 a^{2} b^{6} x^{21}}{3} + \frac {a b^{7} x^{24}}{3} + \frac {b^{8} x^{27}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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