Integrand size = 47, antiderivative size = 21 \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\frac {5 \left (-3+e^{2+\frac {1}{x}-x \log (x)}\right )}{2 x} \]
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Time = 0.04 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules used = {12, 14, 2326} \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\frac {5}{2} e^{\frac {1}{x}+2} x^{-x-1}-\frac {15}{2 x} \]
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Rule 12
Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{x^3} \, dx \\ & = \frac {1}{2} \int \left (\frac {15}{x^2}-5 e^{2+\frac {1}{x}} x^{-3-x} \left (1+x+x^2+x^2 \log (x)\right )\right ) \, dx \\ & = -\frac {15}{2 x}-\frac {5}{2} \int e^{2+\frac {1}{x}} x^{-3-x} \left (1+x+x^2+x^2 \log (x)\right ) \, dx \\ & = -\frac {15}{2 x}+\frac {5}{2} e^{2+\frac {1}{x}} x^{-1-x} \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.24 \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=-\frac {5}{2} \left (\frac {3}{x}-e^{2+\frac {1}{x}} x^{-1-x}\right ) \]
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Time = 0.37 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.29
method | result | size |
risch | \(\frac {5 x^{-x} {\mathrm e}^{\frac {1+2 x}{x}}}{2 x}-\frac {15}{2 x}\) | \(27\) |
parallelrisch | \(-\frac {15-5 \,{\mathrm e}^{-\frac {x^{2} \ln \left (x \right )-2 x -1}{x}}}{2 x}\) | \(27\) |
default | \(\frac {5 \,{\mathrm e}^{\frac {-x^{2} \ln \left (x \right )+2 x +1}{x}}}{2 x}-\frac {15}{2 x}\) | \(29\) |
norman | \(\frac {-\frac {15 x}{2}+\frac {5 x \,{\mathrm e}^{\frac {-x^{2} \ln \left (x \right )+2 x +1}{x}}}{2}}{x^{2}}\) | \(29\) |
parts | \(\frac {5 \,{\mathrm e}^{\frac {-x^{2} \ln \left (x \right )+2 x +1}{x}}}{2 x}-\frac {15}{2 x}\) | \(29\) |
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Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\frac {5 \, {\left (e^{\left (-\frac {x^{2} \log \left (x\right ) - 2 \, x - 1}{x}\right )} - 3\right )}}{2 \, x} \]
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Time = 0.10 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\frac {5 e^{\frac {- x^{2} \log {\left (x \right )} + 2 x + 1}{x}}}{2 x} - \frac {15}{2 x} \]
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.05 \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\frac {5 \, e^{\left (-x \log \left (x\right ) + \frac {1}{x} + 2\right )}}{2 \, x} - \frac {15}{2 \, x} \]
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\[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\int { -\frac {5 \, {\left ({\left (x^{2} \log \left (x\right ) + x^{2} + x + 1\right )} e^{\left (-\frac {x^{2} \log \left (x\right ) - 2 \, x - 1}{x}\right )} - 3 \, x\right )}}{2 \, x^{3}} \,d x } \]
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Time = 9.45 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {15 x+e^{\frac {1+2 x-x^2 \log (x)}{x}} \left (-5-5 x-5 x^2-5 x^2 \log (x)\right )}{2 x^3} \, dx=\frac {5\,\left (\frac {{\mathrm {e}}^{\frac {1}{x}+2}}{x^x}-3\right )}{2\,x} \]
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