Optimal. Leaf size=12 \[ \frac {1}{3} \log \left (a^3+x^3\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, 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 {1}{3} \log \left (a^3+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 266
Rubi steps
\begin {align*} \int \frac {x^2}{a^3+x^3} \, dx &=\frac {1}{3} \log \left (a^3+x^3\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \frac {1}{3} \log \left (a^3+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 11, normalized size = 0.92
method | result | size |
derivativedivides | \(\frac {\ln \left (a^{3}+x^{3}\right )}{3}\) | \(11\) |
default | \(\frac {\ln \left (a^{3}+x^{3}\right )}{3}\) | \(11\) |
risch | \(\frac {\ln \left (a^{3}+x^{3}\right )}{3}\) | \(11\) |
norman | \(\frac {\ln \left (a +x \right )}{3}+\frac {\ln \left (a^{2}-a x +x^{2}\right )}{3}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.77, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{3} \, \log \left (a^{3} + x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{3} \, \log \left (a^{3} + x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.67 \begin {gather*} \frac {\log {\left (a^{3} + x^{3} \right )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.93, size = 11, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, \log \left ({\left | a^{3} + x^{3} \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 10, normalized size = 0.83 \begin {gather*} \frac {\ln \left (a^3+x^3\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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