Optimal. Leaf size=21 \[ a \log (x)+\frac {b x^2}{2}+\frac {c x^4}{4} \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14} \begin {gather*} a \log (x)+\frac {b x^2}{2}+\frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^2+c x^4}{x} \, dx &=\int \left (\frac {a}{x}+b x+c x^3\right ) \, dx\\ &=\frac {b x^2}{2}+\frac {c x^4}{4}+a \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} a \log (x)+\frac {b x^2}{2}+\frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b x^2+c x^4}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 2.11, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{2} \, b x^{2} + a \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 20, normalized size = 0.95 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{2} \, b x^{2} + \frac {1}{2} \, a \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \begin {gather*} \frac {c \,x^{4}}{4}+\frac {b \,x^{2}}{2}+a \ln \relax (x ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 20, normalized size = 0.95 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{2} \, b x^{2} + \frac {1}{2} \, a \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 17, normalized size = 0.81 \begin {gather*} \frac {b\,x^2}{2}+\frac {c\,x^4}{4}+a\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.81 \begin {gather*} a \log {\relax (x )} + \frac {b x^{2}}{2} + \frac {c x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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