Integrand size = 26, antiderivative size = 16 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx=x+e^{x^2} \log (x)-2 (x+\log (x)) \]
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Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {14, 45, 2326} \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx=e^{x^2} \log (x)-x-2 \log (x) \]
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Rule 14
Rule 45
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {-2-x}{x}+\frac {e^{x^2} \left (1+2 x^2 \log (x)\right )}{x}\right ) \, dx \\ & = \int \frac {-2-x}{x} \, dx+\int \frac {e^{x^2} \left (1+2 x^2 \log (x)\right )}{x} \, dx \\ & = e^{x^2} \log (x)+\int \left (-1-\frac {2}{x}\right ) \, dx \\ & = -x-2 \log (x)+e^{x^2} \log (x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx=-x-2 \log (x)+e^{x^2} \log (x) \]
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Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
method | result | size |
default | \({\mathrm e}^{x^{2}} \ln \left (x \right )-x -2 \ln \left (x \right )\) | \(16\) |
norman | \({\mathrm e}^{x^{2}} \ln \left (x \right )-x -2 \ln \left (x \right )\) | \(16\) |
risch | \({\mathrm e}^{x^{2}} \ln \left (x \right )-x -2 \ln \left (x \right )\) | \(16\) |
parallelrisch | \({\mathrm e}^{x^{2}} \ln \left (x \right )-x -2 \ln \left (x \right )\) | \(16\) |
parts | \({\mathrm e}^{x^{2}} \ln \left (x \right )-x -2 \ln \left (x \right )\) | \(16\) |
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none
Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx={\left (e^{\left (x^{2}\right )} - 2\right )} \log \left (x\right ) - x \]
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Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx=- x + e^{x^{2}} \log {\left (x \right )} - 2 \log {\left (x \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx=e^{\left (x^{2}\right )} \log \left (x\right ) - x - 2 \, \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx=e^{\left (x^{2}\right )} \log \left (x\right ) - x - 2 \, \log \left (x\right ) \]
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Time = 7.58 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {-2+e^{x^2}-x+2 e^{x^2} x^2 \log (x)}{x} \, dx={\mathrm {e}}^{x^2}\,\ln \left (x\right )-2\,\ln \left (x\right )-x \]
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