Integrand size = 34, antiderivative size = 22 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=-e^{(-5+x)^2-x}+(3-18 x) \log (x) \]
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Time = 0.03 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {14, 2268, 45, 2332} \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=-e^{x^2-11 x+25}-18 x \log (x)+3 \log (x) \]
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Rule 14
Rule 45
Rule 2268
Rule 2332
Rubi steps \begin{align*} \text {integral}& = \int \left (-e^{25-11 x+x^2} (-11+2 x)-\frac {3 (-1+6 x+6 x \log (x))}{x}\right ) \, dx \\ & = -\left (3 \int \frac {-1+6 x+6 x \log (x)}{x} \, dx\right )-\int e^{25-11 x+x^2} (-11+2 x) \, dx \\ & = -e^{25-11 x+x^2}-3 \int \left (\frac {-1+6 x}{x}+6 \log (x)\right ) \, dx \\ & = -e^{25-11 x+x^2}-3 \int \frac {-1+6 x}{x} \, dx-18 \int \log (x) \, dx \\ & = -e^{25-11 x+x^2}+18 x-18 x \log (x)-3 \int \left (6-\frac {1}{x}\right ) \, dx \\ & = -e^{25-11 x+x^2}+3 \log (x)-18 x \log (x) \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=-e^{25-11 x+x^2}+3 \log (x)-18 x \log (x) \]
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Time = 0.46 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
method | result | size |
norman | \(3 \ln \left (x \right )-18 x \ln \left (x \right )-{\mathrm e}^{x^{2}-11 x +25}\) | \(22\) |
risch | \(3 \ln \left (x \right )-18 x \ln \left (x \right )-{\mathrm e}^{x^{2}-11 x +25}\) | \(22\) |
parallelrisch | \(3 \ln \left (x \right )-18 x \ln \left (x \right )-{\mathrm e}^{x^{2}-11 x +25}\) | \(22\) |
default | \(-\frac {11 i {\mathrm e}^{25} \sqrt {\pi }\, {\mathrm e}^{-\frac {121}{4}} \operatorname {erf}\left (i x -\frac {11}{2} i\right )}{2}-2 \,{\mathrm e}^{25} \left (\frac {{\mathrm e}^{x^{2}-11 x}}{2}-\frac {11 i \sqrt {\pi }\, {\mathrm e}^{-\frac {121}{4}} \operatorname {erf}\left (i x -\frac {11}{2} i\right )}{4}\right )+3 \ln \left (x \right )-18 x \ln \left (x \right )\) | \(60\) |
parts | \(-\frac {11 i {\mathrm e}^{25} \sqrt {\pi }\, {\mathrm e}^{-\frac {121}{4}} \operatorname {erf}\left (i x -\frac {11}{2} i\right )}{2}-2 \,{\mathrm e}^{25} \left (\frac {{\mathrm e}^{x^{2}-11 x}}{2}-\frac {11 i \sqrt {\pi }\, {\mathrm e}^{-\frac {121}{4}} \operatorname {erf}\left (i x -\frac {11}{2} i\right )}{4}\right )+3 \ln \left (x \right )-18 x \ln \left (x \right )\) | \(60\) |
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Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=-3 \, {\left (6 \, x - 1\right )} \log \left (x\right ) - e^{\left (x^{2} - 11 \, x + 25\right )} \]
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Time = 0.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=- 18 x \log {\left (x \right )} - e^{x^{2} - 11 x + 25} + 3 \log {\left (x \right )} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 77, normalized size of antiderivative = 3.50 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=-\frac {11}{2} i \, \sqrt {\pi } \operatorname {erf}\left (i \, x - \frac {11}{2} i\right ) e^{\left (-\frac {21}{4}\right )} - \frac {1}{2} \, {\left (\frac {11 \, \sqrt {\pi } {\left (2 \, x - 11\right )} {\left (\operatorname {erf}\left (\frac {1}{2} \, \sqrt {-{\left (2 \, x - 11\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (2 \, x - 11\right )}^{2}}} + 2 \, e^{\left (\frac {1}{4} \, {\left (2 \, x - 11\right )}^{2}\right )}\right )} e^{\left (-\frac {21}{4}\right )} - 18 \, x \log \left (x\right ) + 3 \, \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=-18 \, x \log \left (x\right ) - e^{\left (x^{2} - 11 \, x + 25\right )} + 3 \, \log \left (x\right ) \]
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Time = 9.66 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {3-18 x+e^{25-11 x+x^2} \left (11 x-2 x^2\right )-18 x \log (x)}{x} \, dx=3\,\ln \left (x\right )-18\,x\,\ln \left (x\right )-{\mathrm {e}}^{-11\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{25} \]
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