Integrand size = 11, antiderivative size = 21 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\frac {2 e^3}{x}-\log \left (-\frac {2}{x \log (2)}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45} \[ \int \frac {-2 e^3+x}{x^2} \, dx=\frac {2 e^3}{x}+\log (x) \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {2 e^3}{x^2}+\frac {1}{x}\right ) \, dx \\ & = \frac {2 e^3}{x}+\log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\frac {2 e^3}{x}+\log (x) \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52
method | result | size |
default | \(\ln \left (x \right )+\frac {2 \,{\mathrm e}^{3}}{x}\) | \(11\) |
norman | \(\ln \left (x \right )+\frac {2 \,{\mathrm e}^{3}}{x}\) | \(11\) |
risch | \(\ln \left (x \right )+\frac {2 \,{\mathrm e}^{3}}{x}\) | \(11\) |
parallelrisch | \(\frac {x \ln \left (x \right )+2 \,{\mathrm e}^{3}}{x}\) | \(14\) |
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none
Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.62 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\frac {x \log \left (x\right ) + 2 \, e^{3}}{x} \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.38 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\log {\left (x \right )} + \frac {2 e^{3}}{x} \]
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none
Time = 0.21 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.48 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\frac {2 \, e^{3}}{x} + \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.52 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\frac {2 \, e^{3}}{x} + \log \left ({\left | x \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.48 \[ \int \frac {-2 e^3+x}{x^2} \, dx=\ln \left (x\right )+\frac {2\,{\mathrm {e}}^3}{x} \]
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