Optimal. Leaf size=15 \[ \frac {\log \left (a+b x^3\right )}{3 b} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {266}
\begin {gather*} \frac {\log \left (a+b x^3\right )}{3 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 266
Rubi steps
\begin {align*} \int \frac {x^2}{a+b x^3} \, dx &=\frac {\log \left (a+b x^3\right )}{3 b}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {\log \left (a+b x^3\right )}{3 b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 14, normalized size = 0.93
method | result | size |
derivativedivides | \(\frac {\ln \left (b \,x^{3}+a \right )}{3 b}\) | \(14\) |
default | \(\frac {\ln \left (b \,x^{3}+a \right )}{3 b}\) | \(14\) |
norman | \(\frac {\ln \left (b \,x^{3}+a \right )}{3 b}\) | \(14\) |
risch | \(\frac {\ln \left (b \,x^{3}+a \right )}{3 b}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (b x^{3} + a\right )}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.87 \begin {gather*} \frac {\log \left (b x^{3} + a\right )}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} \frac {\log {\left (a + b x^{3} \right )}}{3 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.87, size = 14, normalized size = 0.93 \begin {gather*} \frac {\log \left ({\left | b x^{3} + a \right |}\right )}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 13, normalized size = 0.87 \begin {gather*} \frac {\ln \left (b\,x^3+a\right )}{3\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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