Integrand size = 31, antiderivative size = 18 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=(-x+\log (2)) \left (8-\frac {29 x}{14}+\log \left (\frac {1}{x}\right )\right ) \]
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Time = 0.02 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.94, number of steps used = 6, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 14, 2332} \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=\frac {29 x^2}{14}-x-x \log \left (\frac {1}{x}\right )-\frac {1}{14} x (98+29 \log (2))-\log (2) \log (x) \]
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Rule 12
Rule 14
Rule 2332
Rubi steps \begin{align*} \text {integral}& = \frac {1}{14} \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{x} \, dx \\ & = \frac {1}{14} \int \left (\frac {58 x^2-14 \log (2)-x (98+29 \log (2))}{x}-14 \log \left (\frac {1}{x}\right )\right ) \, dx \\ & = \frac {1}{14} \int \frac {58 x^2-14 \log (2)-x (98+29 \log (2))}{x} \, dx-\int \log \left (\frac {1}{x}\right ) \, dx \\ & = -x-x \log \left (\frac {1}{x}\right )+\frac {1}{14} \int \left (-98+58 x-29 \log (2)-\frac {14 \log (2)}{x}\right ) \, dx \\ & = -x+\frac {29 x^2}{14}-\frac {1}{14} x (98+29 \log (2))-x \log \left (\frac {1}{x}\right )-\log (2) \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=-8 x+\frac {29 x^2}{14}-\frac {29}{14} x \log (2)-x \log \left (\frac {1}{x}\right )-\log (2) \log (x) \]
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Time = 0.19 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.56
method | result | size |
risch | \(-x \ln \left (\frac {1}{x}\right )-\frac {29 x \ln \left (2\right )}{14}+\frac {29 x^{2}}{14}-8 x -\ln \left (2\right ) \ln \left (x \right )\) | \(28\) |
parts | \(-x \ln \left (\frac {1}{x}\right )-\frac {29 x \ln \left (2\right )}{14}+\frac {29 x^{2}}{14}-8 x -\ln \left (2\right ) \ln \left (x \right )\) | \(28\) |
derivativedivides | \(\ln \left (2\right ) \ln \left (\frac {1}{x}\right )-\frac {29 x \ln \left (2\right )}{14}-x \ln \left (\frac {1}{x}\right )-8 x +\frac {29 x^{2}}{14}\) | \(29\) |
default | \(\ln \left (2\right ) \ln \left (\frac {1}{x}\right )-\frac {29 x \ln \left (2\right )}{14}-x \ln \left (\frac {1}{x}\right )-8 x +\frac {29 x^{2}}{14}\) | \(29\) |
norman | \(\left (-8-\frac {29 \ln \left (2\right )}{14}\right ) x +\ln \left (2\right ) \ln \left (\frac {1}{x}\right )+\frac {29 x^{2}}{14}-x \ln \left (\frac {1}{x}\right )\) | \(29\) |
parallelrisch | \(\ln \left (2\right ) \ln \left (\frac {1}{x}\right )-\frac {29 x \ln \left (2\right )}{14}-x \ln \left (\frac {1}{x}\right )-8 x +\frac {29 x^{2}}{14}\) | \(29\) |
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Time = 0.28 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.44 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=\frac {29}{14} \, x^{2} - \frac {29}{14} \, x \log \left (2\right ) - {\left (x - \log \left (2\right )\right )} \log \left (\frac {1}{x}\right ) - 8 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (15) = 30\).
Time = 0.09 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=\frac {29 x^{2}}{14} - x \log {\left (\frac {1}{x} \right )} + \frac {x \left (-112 - 29 \log {\left (2 \right )}\right )}{14} - \log {\left (2 \right )} \log {\left (x \right )} \]
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Time = 0.21 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.33 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=\frac {29}{14} \, x^{2} - \frac {29}{14} \, x \log \left (2\right ) + x \log \left (x\right ) - \log \left (2\right ) \log \left (x\right ) - 8 \, x \]
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Time = 0.29 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.39 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=\frac {29}{14} \, x^{2} - \frac {1}{14} \, x {\left (29 \, \log \left (2\right ) + 112\right )} + x \log \left (x\right ) - \log \left (2\right ) \log \left (x\right ) \]
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Time = 11.12 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.56 \[ \int \frac {-98 x+58 x^2+(-14-29 x) \log (2)-14 x \log \left (\frac {1}{x}\right )}{14 x} \, dx=\ln \left (\frac {1}{x}\right )\,\ln \left (2\right )-8\,x-x\,\ln \left (\frac {1}{x}\right )-\frac {29\,x\,\ln \left (2\right )}{14}+\frac {29\,x^2}{14} \]
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