Integrand size = 10, antiderivative size = 11 \[ \int \frac {e^2}{3 x} \, dx=-14+\frac {1}{3} e^2 \log (x) \]
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Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 29} \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} e^2 \log (x) \]
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Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} e^2 \int \frac {1}{x} \, dx \\ & = \frac {1}{3} e^2 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} e^2 \log (x) \]
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Time = 0.09 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64
method | result | size |
default | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
norman | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
risch | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
parallelrisch | \(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\) | \(7\) |
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} \, e^{2} \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {e^2}{3 x} \, dx=\frac {e^{2} \log {\left (x \right )}}{3} \]
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none
Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} \, e^{2} \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} \, e^{2} \log \left ({\left | x \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {e^2}{3 x} \, dx=\frac {{\mathrm {e}}^2\,\ln \left (x\right )}{3} \]
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