Integrand size = 6, antiderivative size = 17 \[ \int x^2 \log (x) \, dx=-\frac {x^3}{9}+\frac {1}{3} x^3 \log (x) \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2341} \[ \int x^2 \log (x) \, dx=\frac {1}{3} x^3 \log (x)-\frac {x^3}{9} \]
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Rule 2341
Rubi steps \begin{align*} \text {integral}& = -\frac {x^3}{9}+\frac {1}{3} x^3 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int x^2 \log (x) \, dx=-\frac {x^3}{9}+\frac {1}{3} x^3 \log (x) \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82
method | result | size |
default | \(-\frac {x^{3}}{9}+\frac {x^{3} \ln \left (x \right )}{3}\) | \(14\) |
norman | \(-\frac {x^{3}}{9}+\frac {x^{3} \ln \left (x \right )}{3}\) | \(14\) |
risch | \(-\frac {x^{3}}{9}+\frac {x^{3} \ln \left (x \right )}{3}\) | \(14\) |
parallelrisch | \(-\frac {x^{3}}{9}+\frac {x^{3} \ln \left (x \right )}{3}\) | \(14\) |
parts | \(-\frac {x^{3}}{9}+\frac {x^{3} \ln \left (x \right )}{3}\) | \(14\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x^2 \log (x) \, dx=\frac {1}{3} \, x^{3} \log \left (x\right ) - \frac {1}{9} \, x^{3} \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71 \[ \int x^2 \log (x) \, dx=\frac {x^{3} \log {\left (x \right )}}{3} - \frac {x^{3}}{9} \]
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none
Time = 0.18 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x^2 \log (x) \, dx=\frac {1}{3} \, x^{3} \log \left (x\right ) - \frac {1}{9} \, x^{3} \]
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none
Time = 0.28 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int x^2 \log (x) \, dx=\frac {1}{3} \, x^{3} \log \left (x\right ) - \frac {1}{9} \, x^{3} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.53 \[ \int x^2 \log (x) \, dx=\frac {x^3\,\left (\ln \left (x\right )-\frac {1}{3}\right )}{3} \]
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