Integrand size = 18, antiderivative size = 14 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=x+(1-x) (x-\log (x)) \]
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Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.21, number of steps used = 5, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {14, 2332} \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=-x^2+2 x+x \log (x)-\log (x) \]
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Rule 14
Rule 2332
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {-1+3 x-2 x^2}{x}+\log (x)\right ) \, dx \\ & = \int \frac {-1+3 x-2 x^2}{x} \, dx+\int \log (x) \, dx \\ & = -x+x \log (x)+\int \left (3-\frac {1}{x}-2 x\right ) \, dx \\ & = 2 x-x^2-\log (x)+x \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.21 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=2 x-x^2-\log (x)+x \log (x) \]
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Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.29
method | result | size |
default | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
norman | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
risch | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
parallelrisch | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
parts | \(x \ln \left (x \right )+2 x -x^{2}-\ln \left (x \right )\) | \(18\) |
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none
Time = 0.24 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=-x^{2} + {\left (x - 1\right )} \log \left (x\right ) + 2 \, x \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=- x^{2} + x \log {\left (x \right )} + 2 x - \log {\left (x \right )} \]
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none
Time = 0.17 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.21 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=-x^{2} + x \log \left (x\right ) + 2 \, x - \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.21 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=-x^{2} + x \log \left (x\right ) + 2 \, x - \log \left (x\right ) \]
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Time = 7.36 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.21 \[ \int \frac {-1+3 x-2 x^2+x \log (x)}{x} \, dx=2\,x-\ln \left (x\right )+x\,\ln \left (x\right )-x^2 \]
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