Integrand size = 25, antiderivative size = 24 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=-3 e^x-e^{x^3}+2 x+\log (2)-\log \left (x^2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 8, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.160, Rules used = {14, 2240, 2225, 45} \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=-e^{x^3}+2 x-3 e^x-2 \log (x) \]
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Rule 14
Rule 45
Rule 2225
Rule 2240
Rubi steps \begin{align*} \text {integral}& = \int \left (-3 e^{x^3} x^2-\frac {2-2 x+3 e^x x}{x}\right ) \, dx \\ & = -\left (3 \int e^{x^3} x^2 \, dx\right )-\int \frac {2-2 x+3 e^x x}{x} \, dx \\ & = -e^{x^3}-\int \left (3 e^x-\frac {2 (-1+x)}{x}\right ) \, dx \\ & = -e^{x^3}+2 \int \frac {-1+x}{x} \, dx-3 \int e^x \, dx \\ & = -3 e^x-e^{x^3}+2 \int \left (1-\frac {1}{x}\right ) \, dx \\ & = -3 e^x-e^{x^3}+2 x-2 \log (x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=-3 e^x-e^{x^3}+2 x-2 \log (x) \]
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Time = 0.36 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79
method | result | size |
default | \(2 x -2 \ln \left (x \right )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
norman | \(2 x -2 \ln \left (x \right )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
risch | \(2 x -2 \ln \left (x \right )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
parallelrisch | \(2 x -2 \ln \left (x \right )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
parts | \(2 x -2 \ln \left (x \right )-{\mathrm e}^{x^{3}}-3 \,{\mathrm e}^{x}\) | \(19\) |
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Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=2 \, x - e^{\left (x^{3}\right )} - 3 \, e^{x} - 2 \, \log \left (x\right ) \]
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Time = 0.09 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=2 x - 3 e^{x} - e^{x^{3}} - 2 \log {\left (x \right )} \]
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Time = 0.19 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=2 \, x - e^{\left (x^{3}\right )} - 3 \, e^{x} - 2 \, \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=2 \, x - e^{\left (x^{3}\right )} - 3 \, e^{x} - 2 \, \log \left (x\right ) \]
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Time = 9.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {-2+2 x-3 e^x x-3 e^{x^3} x^3}{x} \, dx=2\,x-{\mathrm {e}}^{x^3}-3\,{\mathrm {e}}^x-2\,\ln \left (x\right ) \]
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