Optimal. Leaf size=30 \[ \frac {a^2 x^5}{5}+\frac {1}{4} a b x^8+\frac {b^2 x^{11}}{11} \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ \frac {a^2 x^5}{5}+\frac {1}{4} a b x^8+\frac {b^2 x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int x^4 \left (a+b x^3\right )^2 \, dx &=\int \left (a^2 x^4+2 a b x^7+b^2 x^{10}\right ) \, dx\\ &=\frac {a^2 x^5}{5}+\frac {1}{4} a b x^8+\frac {b^2 x^{11}}{11}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ \frac {a^2 x^5}{5}+\frac {1}{4} a b x^8+\frac {b^2 x^{11}}{11} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 24, normalized size = 0.80 \[ \frac {1}{11} x^{11} b^{2} + \frac {1}{4} x^{8} b a + \frac {1}{5} x^{5} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.80 \[ \frac {1}{11} \, b^{2} x^{11} + \frac {1}{4} \, a b x^{8} + \frac {1}{5} \, a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \[ \frac {1}{11} b^{2} x^{11}+\frac {1}{4} a b \,x^{8}+\frac {1}{5} a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 24, normalized size = 0.80 \[ \frac {1}{11} \, b^{2} x^{11} + \frac {1}{4} \, a b x^{8} + \frac {1}{5} \, a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 24, normalized size = 0.80 \[ \frac {a^2\,x^5}{5}+\frac {a\,b\,x^8}{4}+\frac {b^2\,x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 24, normalized size = 0.80 \[ \frac {a^{2} x^{5}}{5} + \frac {a b x^{8}}{4} + \frac {b^{2} x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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