Optimal. Leaf size=13 \[ b \log (x)+\frac {c x^2}{2} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \[ b \log (x)+\frac {c x^2}{2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x^3} \, dx &=\int \left (\frac {b}{x}+c x\right ) \, dx\\ &=\frac {c x^2}{2}+b \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ b \log (x)+\frac {c x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 11, normalized size = 0.85 \[ \frac {1}{2} \, c x^{2} + b \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 1.08 \[ \frac {1}{2} \, c x^{2} + \frac {1}{2} \, b \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.92 \[ \frac {c \,x^{2}}{2}+b \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 14, normalized size = 1.08 \[ \frac {1}{2} \, c x^{2} + \frac {1}{2} \, b \log \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.85 \[ \frac {c\,x^2}{2}+b\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.77 \[ b \log {\relax (x )} + \frac {c x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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