Integrand size = 14, antiderivative size = 16 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2+2 x+2 x^2-\log \left (x^2\right ) \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14} \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2 x^2+2 x-2 \log (x) \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (2-\frac {2}{x}+4 x\right ) \, dx \\ & = 2 x+2 x^2-2 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2 x+2 x^2-2 \log (x) \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88
method | result | size |
default | \(2 x^{2}-2 \ln \left (x \right )+2 x\) | \(14\) |
norman | \(2 x^{2}-2 \ln \left (x \right )+2 x\) | \(14\) |
risch | \(2 x^{2}-2 \ln \left (x \right )+2 x\) | \(14\) |
parallelrisch | \(2 x^{2}-2 \ln \left (x \right )+2 x\) | \(14\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2 \, x^{2} + 2 \, x - 2 \, \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2 x^{2} + 2 x - 2 \log {\left (x \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2 \, x^{2} + 2 \, x - 2 \, \log \left (x\right ) \]
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none
Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2 \, x^{2} + 2 \, x - 2 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {-2+2 x+4 x^2}{x} \, dx=2\,x-2\,\ln \left (x\right )+2\,x^2 \]
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