Integrand size = 10, antiderivative size = 12 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \left (-5+\log \left (\frac {3 x^3}{125}\right )\right ) \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2332} \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3 x^3}{125}\right )-5 x \]
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Rule 2332
Rubi steps \begin{align*} \text {integral}& = -2 x+\int \log \left (\frac {3 x^3}{125}\right ) \, dx \\ & = -5 x+x \log \left (\frac {3 x^3}{125}\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=-5 x+x \log \left (\frac {3 x^3}{125}\right ) \]
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Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08
method | result | size |
norman | \(x \ln \left (\frac {3 x^{3}}{125}\right )-5 x\) | \(13\) |
risch | \(x \ln \left (\frac {3 x^{3}}{125}\right )-5 x\) | \(13\) |
parallelrisch | \(x \ln \left (\frac {3 x^{3}}{125}\right )-5 x\) | \(13\) |
default | \(-5 x -3 x \ln \left (5\right )+x \ln \left (3\right )+x \ln \left (x^{3}\right )\) | \(20\) |
parts | \(-5 x -3 x \ln \left (5\right )+x \ln \left (3\right )+x \ln \left (x^{3}\right )\) | \(20\) |
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none
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3}{125} \, x^{3}\right ) - 5 \, x \]
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Time = 0.07 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log {\left (\frac {3 x^{3}}{125} \right )} - 5 x \]
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none
Time = 0.18 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3}{125} \, x^{3}\right ) - 5 \, x \]
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none
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x \log \left (\frac {3}{125} \, x^{3}\right ) - 5 \, x \]
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Time = 9.99 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (-2+\log \left (\frac {3 x^3}{125}\right )\right ) \, dx=x\,\left (\ln \left (\frac {3\,x^3}{125}\right )-5\right ) \]
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