Integrand size = 15, antiderivative size = 14 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=3+x-x^2+\log (5)+\log ^2(x) \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {14, 2338} \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=-x^2+x+\log ^2(x) \]
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Rule 14
Rule 2338
Rubi steps \begin{align*} \text {integral}& = \int \left (1-2 x+\frac {2 \log (x)}{x}\right ) \, dx \\ & = x-x^2+2 \int \frac {\log (x)}{x} \, dx \\ & = x-x^2+\log ^2(x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=x-x^2+\log ^2(x) \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86
method | result | size |
default | \(\ln \left (x \right )^{2}-x^{2}+x\) | \(12\) |
norman | \(\ln \left (x \right )^{2}-x^{2}+x\) | \(12\) |
risch | \(\ln \left (x \right )^{2}-x^{2}+x\) | \(12\) |
parallelrisch | \(\ln \left (x \right )^{2}-x^{2}+x\) | \(12\) |
parts | \(\ln \left (x \right )^{2}-x^{2}+x\) | \(12\) |
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none
Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=-x^{2} + \log \left (x\right )^{2} + x \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.57 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=- x^{2} + x + \log {\left (x \right )}^{2} \]
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none
Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=-x^{2} + \log \left (x\right )^{2} + x \]
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=-x^{2} + \log \left (x\right )^{2} + x \]
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Time = 11.73 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {x-2 x^2+2 \log (x)}{x} \, dx=-x^2+x+{\ln \left (x\right )}^2 \]
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