Optimal. Leaf size=43 \[ \frac {a^3 x^{10}}{10}+\frac {1}{4} a^2 b x^{12}+\frac {3}{14} a b^2 x^{14}+\frac {b^3 x^{16}}{16} \]
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Rubi [A] time = 0.03, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {1}{4} a^2 b x^{12}+\frac {a^3 x^{10}}{10}+\frac {3}{14} a b^2 x^{14}+\frac {b^3 x^{16}}{16} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int x^9 \left (a+b x^2\right )^3 \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int x^4 (a+b x)^3 \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (a^3 x^4+3 a^2 b x^5+3 a b^2 x^6+b^3 x^7\right ) \, dx,x,x^2\right )\\ &=\frac {a^3 x^{10}}{10}+\frac {1}{4} a^2 b x^{12}+\frac {3}{14} a b^2 x^{14}+\frac {b^3 x^{16}}{16}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ \frac {a^3 x^{10}}{10}+\frac {1}{4} a^2 b x^{12}+\frac {3}{14} a b^2 x^{14}+\frac {b^3 x^{16}}{16} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 35, normalized size = 0.81 \[ \frac {1}{16} x^{16} b^{3} + \frac {3}{14} x^{14} b^{2} a + \frac {1}{4} x^{12} b a^{2} + \frac {1}{10} x^{10} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 35, normalized size = 0.81 \[ \frac {1}{16} \, b^{3} x^{16} + \frac {3}{14} \, a b^{2} x^{14} + \frac {1}{4} \, a^{2} b x^{12} + \frac {1}{10} \, a^{3} x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ \frac {1}{16} b^{3} x^{16}+\frac {3}{14} a \,b^{2} x^{14}+\frac {1}{4} a^{2} b \,x^{12}+\frac {1}{10} a^{3} x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 35, normalized size = 0.81 \[ \frac {1}{16} \, b^{3} x^{16} + \frac {3}{14} \, a b^{2} x^{14} + \frac {1}{4} \, a^{2} b x^{12} + \frac {1}{10} \, a^{3} x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.81 \[ \frac {a^3\,x^{10}}{10}+\frac {a^2\,b\,x^{12}}{4}+\frac {3\,a\,b^2\,x^{14}}{14}+\frac {b^3\,x^{16}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 37, normalized size = 0.86 \[ \frac {a^{3} x^{10}}{10} + \frac {a^{2} b x^{12}}{4} + \frac {3 a b^{2} x^{14}}{14} + \frac {b^{3} x^{16}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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