Integrand size = 10, antiderivative size = 11 \[ \int \frac {1+x+x^2}{x} \, dx=x+\frac {x^2}{2}+\log (x) \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14} \[ \int \frac {1+x+x^2}{x} \, dx=\frac {x^2}{2}+x+\log (x) \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (1+\frac {1}{x}+x\right ) \, dx \\ & = x+\frac {x^2}{2}+\log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {1+x+x^2}{x} \, dx=x+\frac {x^2}{2}+\log (x) \]
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Time = 0.10 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91
method | result | size |
default | \(x +\frac {x^{2}}{2}+\ln \left (x \right )\) | \(10\) |
norman | \(x +\frac {x^{2}}{2}+\ln \left (x \right )\) | \(10\) |
risch | \(x +\frac {x^{2}}{2}+\ln \left (x \right )\) | \(10\) |
parallelrisch | \(x +\frac {x^{2}}{2}+\ln \left (x \right )\) | \(10\) |
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none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {1+x+x^2}{x} \, dx=\frac {1}{2} \, x^{2} + x + \log \left (x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {1+x+x^2}{x} \, dx=\frac {x^{2}}{2} + x + \log {\left (x \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {1+x+x^2}{x} \, dx=\frac {1}{2} \, x^{2} + x + \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {1+x+x^2}{x} \, dx=\frac {1}{2} \, x^{2} + x + \log \left ({\left | x \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {1+x+x^2}{x} \, dx=x+\ln \left (x\right )+\frac {x^2}{2} \]
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