Optimal. Leaf size=25 \[ \frac {a x^4}{4}+\frac {b x^6}{6}+\frac {c x^8}{8} \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \begin {gather*} \frac {a x^4}{4}+\frac {b x^6}{6}+\frac {c x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^2 \left (a x+b x^3+c x^5\right ) \, dx &=\int \left (a x^3+b x^5+c x^7\right ) \, dx\\ &=\frac {a x^4}{4}+\frac {b x^6}{6}+\frac {c x^8}{8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} \frac {a x^4}{4}+\frac {b x^6}{6}+\frac {c x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \left (a x+b x^3+c x^5\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.99, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{8} x^{8} c + \frac {1}{6} x^{6} b + \frac {1}{4} x^{4} a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{8} \, c x^{8} + \frac {1}{6} \, b x^{6} + \frac {1}{4} \, a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{8} c \,x^{8}+\frac {1}{6} b \,x^{6}+\frac {1}{4} a \,x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{8} \, c x^{8} + \frac {1}{6} \, b x^{6} + \frac {1}{4} \, a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} \frac {c\,x^8}{8}+\frac {b\,x^6}{6}+\frac {a\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 0.76 \begin {gather*} \frac {a x^{4}}{4} + \frac {b x^{6}}{6} + \frac {c x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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