Integrand size = 55, antiderivative size = 23 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5}{4} e^{x^2-\left (1+e^x-x\right ) x^{12}} \]
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Time = 0.21 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 6838} \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5}{4} e^{x^{13}-e^x x^{12}-x^{12}+x^2} \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \int e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx \\ & = \frac {5}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \\ \end{align*}
Time = 0.86 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5}{4} e^{x^2-\left (1+e^x\right ) x^{12}+x^{13}} \]
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Time = 0.46 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00
method | result | size |
parallelrisch | \(\frac {5 \,{\mathrm e}^{-x^{12} {\mathrm e}^{x}+x^{13}-x^{12}+x^{2}}}{4}\) | \(23\) |
risch | \(\frac {5 \,{\mathrm e}^{-x^{2} \left ({\mathrm e}^{x} x^{10}-x^{11}+x^{10}-1\right )}}{4}\) | \(25\) |
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5}{4} \, e^{\left (x^{13} - x^{12} e^{x} - x^{12} + x^{2}\right )} \]
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Time = 0.12 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5 e^{x^{13} - x^{12} e^{x} - x^{12} + x^{2}}}{4} \]
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Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5}{4} \, e^{\left (x^{13} - x^{12} e^{x} - x^{12} + x^{2}\right )} \]
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Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5}{4} \, e^{\left (x^{13} - x^{12} e^{x} - x^{12} + x^{2}\right )} \]
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Time = 12.59 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {1}{4} e^{x^2-x^{12}-e^x x^{12}+x^{13}} \left (10 x-60 x^{11}+65 x^{12}+e^x \left (-60 x^{11}-5 x^{12}\right )\right ) \, dx=\frac {5\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{x^{13}}\,{\mathrm {e}}^{-x^{12}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x^{12}}}{4} \]
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