Integrand size = 7, antiderivative size = 10 \[ \int \frac {1}{e^6 x} \, dx=8+\frac {4+\log (x)}{e^6} \]
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Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 29} \[ \int \frac {1}{e^6 x} \, dx=\frac {\log (x)}{e^6} \]
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Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {1}{x} \, dx}{e^6} \\ & = \frac {\log (x)}{e^6} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60 \[ \int \frac {1}{e^6 x} \, dx=\frac {\log (x)}{e^6} \]
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Time = 0.14 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60
method | result | size |
risch | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(6\) |
default | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(8\) |
norman | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(8\) |
parallelrisch | \({\mathrm e}^{-6} \ln \left (x \right )\) | \(8\) |
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none
Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx=e^{\left (-6\right )} \log \left (x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx=\frac {\log {\left (x \right )}}{e^{6}} \]
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none
Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx=e^{\left (-6\right )} \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60 \[ \int \frac {1}{e^6 x} \, dx=e^{\left (-6\right )} \log \left ({\left | x \right |}\right ) \]
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Time = 15.06 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx={\mathrm {e}}^{-6}\,\ln \left (x\right ) \]
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