Integrand size = 19, antiderivative size = 20 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=\frac {4 \left (-x-\frac {x^2}{2}\right ) (x+\log (x))}{x} \]
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Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps used = 5, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {14, 2332} \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=-2 x^2-4 x-2 x \log (x)-4 \log (x) \]
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Rule 14
Rule 2332
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {2 \left (2+3 x+2 x^2\right )}{x}-2 \log (x)\right ) \, dx \\ & = -\left (2 \int \frac {2+3 x+2 x^2}{x} \, dx\right )-2 \int \log (x) \, dx \\ & = 2 x-2 x \log (x)-2 \int \left (3+\frac {2}{x}+2 x\right ) \, dx \\ & = -4 x-2 x^2-4 \log (x)-2 x \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=-4 x-2 x^2-4 \log (x)-2 x \log (x) \]
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Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95
method | result | size |
default | \(-4 x -2 x \ln \left (x \right )-2 x^{2}-4 \ln \left (x \right )\) | \(19\) |
norman | \(-4 x -2 x \ln \left (x \right )-2 x^{2}-4 \ln \left (x \right )\) | \(19\) |
risch | \(-4 x -2 x \ln \left (x \right )-2 x^{2}-4 \ln \left (x \right )\) | \(19\) |
parallelrisch | \(-4 x -2 x \ln \left (x \right )-2 x^{2}-4 \ln \left (x \right )\) | \(19\) |
parts | \(-4 x -2 x \ln \left (x \right )-2 x^{2}-4 \ln \left (x \right )\) | \(19\) |
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Time = 0.23 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=-2 \, x^{2} - 2 \, {\left (x + 2\right )} \log \left (x\right ) - 4 \, x \]
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Time = 0.07 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=- 2 x^{2} - 2 x \log {\left (x \right )} - 4 x - 4 \log {\left (x \right )} \]
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Time = 0.19 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=-2 \, x^{2} - 2 \, x \log \left (x\right ) - 4 \, x - 4 \, \log \left (x\right ) \]
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Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=-2 \, x^{2} - 2 \, x \log \left (x\right ) - 4 \, x - 4 \, \log \left (x\right ) \]
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Time = 9.94 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {-4-6 x-4 x^2-2 x \log (x)}{x} \, dx=-2\,\left (x+\ln \left (x\right )\right )\,\left (x+2\right ) \]
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