Integrand size = 13, antiderivative size = 12 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {1}{12} \log \left (2+3 x^4\right ) \]
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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} \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {1}{12} \log \left (3 x^4+2\right ) \]
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Rule 266
Rubi steps \begin{align*} \text {integral}& = \frac {1}{12} \log \left (2+3 x^4\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {1}{12} \log \left (2+3 x^4\right ) \]
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Time = 3.91 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75
method | result | size |
parallelrisch | \(\frac {\ln \left (x^{4}+\frac {2}{3}\right )}{12}\) | \(9\) |
derivativedivides | \(\frac {\ln \left (3 x^{4}+2\right )}{12}\) | \(11\) |
default | \(\frac {\ln \left (3 x^{4}+2\right )}{12}\) | \(11\) |
norman | \(\frac {\ln \left (3 x^{4}+2\right )}{12}\) | \(11\) |
meijerg | \(\frac {\ln \left (\frac {3 x^{4}}{2}+1\right )}{12}\) | \(11\) |
risch | \(\frac {\ln \left (3 x^{4}+2\right )}{12}\) | \(11\) |
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {\log {\left (3 x^{4} + 2 \right )}}{12} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]
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none
Time = 0.33 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {1}{12} \, \log \left (3 \, x^{4} + 2\right ) \]
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Time = 5.63 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x^3}{2+3 x^4} \, dx=\frac {\ln \left (x^4+\frac {2}{3}\right )}{12} \]
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