Integrand size = 6, antiderivative size = 7 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} x \log (3) \]
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Time = 0.00 (sec) , antiderivative size = 7, 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 = {8} \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} x \log (3) \]
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Rule 8
Rubi steps \begin{align*} \text {integral}& = -\frac {1}{3} x \log (3) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} x \log (3) \]
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Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86
method | result | size |
default | \(-\frac {x \ln \left (3\right )}{3}\) | \(6\) |
norman | \(-\frac {x \ln \left (3\right )}{3}\) | \(6\) |
risch | \(-\frac {x \ln \left (3\right )}{3}\) | \(6\) |
parallelrisch | \(-\frac {x \ln \left (3\right )}{3}\) | \(6\) |
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none
Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} \, x \log \left (3\right ) \]
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Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int -\frac {\log (3)}{3} \, dx=- \frac {x \log {\left (3 \right )}}{3} \]
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none
Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} \, x \log \left (3\right ) \]
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none
Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} \, x \log \left (3\right ) \]
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Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {x\,\ln \left (3\right )}{3} \]
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