Optimal. Leaf size=16 \[ \frac {1}{8} \left (x^4+4 x^2+1\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {1588} \[ \frac {1}{8} \left (x^4+4 x^2+1\right )^2 \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \left (2 x+x^3\right ) \left (1+4 x^2+x^4\right ) \, dx &=\frac {1}{8} \left (1+4 x^2+x^4\right )^2\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.31 \[ \frac {x^8}{8}+x^6+\frac {9 x^4}{4}+x^2 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 17, normalized size = 1.06 \[ \frac {1}{8} x^{8} + x^{6} + \frac {9}{4} x^{4} + x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 22, normalized size = 1.38 \[ \frac {1}{4} \, x^{4} + \frac {1}{8} \, {\left (x^{4} + 4 \, x^{2}\right )}^{2} + x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 1.12 \[ \frac {1}{8} x^{8}+x^{6}+\frac {9}{4} x^{4}+x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 14, normalized size = 0.88 \[ \frac {1}{8} \, {\left (x^{4} + 4 \, x^{2} + 1\right )}^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 17, normalized size = 1.06 \[ \frac {x^8}{8}+x^6+\frac {9\,x^4}{4}+x^2 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 1.06 \[ \frac {x^{8}}{8} + x^{6} + \frac {9 x^{4}}{4} + x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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