Optimal. Leaf size=13 \[ \frac {b x^3}{3}+a \log (x) \]
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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}
\begin {gather*} a \log (x)+\frac {b x^3}{3} \end {gather*}
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 \begin {gather*} \frac {b x^3}{3}+a \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 0.92
method | result | size |
default | \(\frac {b \,x^{3}}{3}+a \ln \left (x \right )\) | \(12\) |
norman | \(\frac {b \,x^{3}}{3}+a \ln \left (x \right )\) | \(12\) |
risch | \(\frac {b \,x^{3}}{3}+a \ln \left (x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 14, normalized size = 1.08 \begin {gather*} \frac {1}{3} \, b x^{3} + \frac {1}{3} \, a \log \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, b x^{3} + a \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.77 \begin {gather*} a \log {\left (x \right )} + \frac {b x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.20, size = 12, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, b x^{3} + a \log \left ({\left | x \right |}\right ) \end {gather*}
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 \begin {gather*} \frac {b\,x^3}{3}+a\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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