Integrand size = 16, antiderivative size = 15 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=\frac {1}{5} \left (3-3 x^2 \log (5)+\log (x)\right ) \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14} \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=\frac {\log (x)}{5}-\frac {3}{5} x^2 \log (5) \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \frac {1-6 x^2 \log (5)}{x} \, dx \\ & = \frac {1}{5} \int \left (\frac {1}{x}-6 x \log (5)\right ) \, dx \\ & = -\frac {3}{5} x^2 \log (5)+\frac {\log (x)}{5} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=-\frac {3}{5} x^2 \log (5)+\frac {\log (x)}{5} \]
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Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87
method | result | size |
default | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
norman | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
risch | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
parallelrisch | \(-\frac {3 x^{2} \ln \left (5\right )}{5}+\frac {\ln \left (x \right )}{5}\) | \(13\) |
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none
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=-\frac {3}{5} \, x^{2} \log \left (5\right ) + \frac {1}{5} \, \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=- \frac {3 x^{2} \log {\left (5 \right )}}{5} + \frac {\log {\left (x \right )}}{5} \]
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none
Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=-\frac {3}{5} \, x^{2} \log \left (5\right ) + \frac {1}{10} \, \log \left (x^{2}\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=-\frac {3}{5} \, x^{2} \log \left (5\right ) + \frac {1}{10} \, \log \left (x^{2}\right ) \]
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Time = 8.15 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {1-6 x^2 \log (5)}{5 x} \, dx=\frac {\ln \left (x\right )}{5}-\frac {3\,x^2\,\ln \left (5\right )}{5} \]
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