Optimal. Leaf size=13 \[ a \log (x)+\frac {b x^3}{3} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ a \log (x)+\frac {b x^3}{3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^3}{x} \, dx &=\int \left (\frac {a}{x}+b x^2\right ) \, dx\\ &=\frac {b x^3}{3}+a \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ a \log (x)+\frac {b x^3}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 11, normalized size = 0.85 \[ \frac {1}{3} \, b x^{3} + a \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 12, normalized size = 0.92 \[ \frac {1}{3} \, b x^{3} + a \log \left ({\left | x \right |}\right ) \]
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 \[ \frac {b \,x^{3}}{3}+a \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.25, size = 14, normalized size = 1.08 \[ \frac {1}{3} \, b x^{3} + \frac {1}{3} \, a \log \left (x^{3}\right ) \]
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 \[ \frac {b\,x^3}{3}+a\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 10, normalized size = 0.77 \[ a \log {\relax (x )} + \frac {b x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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