Integrand size = 13, antiderivative size = 12 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {1}{3} \log \left (a^3+x^3\right ) \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {266} \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {1}{3} \log \left (a^3+x^3\right ) \]
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Rule 266
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \log \left (a^3+x^3\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {1}{3} \log \left (a^3+x^3\right ) \]
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Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 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 | \(\frac {\ln \left (a +x \right )}{3}+\frac {\ln \left (a^{2}-a x +x^{2}\right )}{3}\) | \(22\) |
parallelrisch | \(\frac {\ln \left (a +x \right )}{3}+\frac {\ln \left (a^{2}-a x +x^{2}\right )}{3}\) | \(22\) |
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none
Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {1}{3} \, \log \left (a^{3} + x^{3}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {\log {\left (a^{3} + x^{3} \right )}}{3} \]
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none
Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {1}{3} \, \log \left (a^{3} + x^{3}\right ) \]
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none
Time = 0.29 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {1}{3} \, \log \left ({\left | a^{3} + x^{3} \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x^2}{a^3+x^3} \, dx=\frac {\ln \left (a^3+x^3\right )}{3} \]
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