Integrand size = 45, antiderivative size = 21 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=\frac {4 e^{-20 (-1+x)+x}}{\log \left (2-\frac {33 x}{32}\right )} \]
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Time = 0.08 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {2326} \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=\frac {4 e^{20-19 x}}{\log \left (\frac {1}{32} (64-33 x)\right )} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {4 e^{20-19 x}}{\log \left (\frac {1}{32} (64-33 x)\right )} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=\frac {4 e^{20-19 x}}{\log \left (2-\frac {33 x}{32}\right )} \]
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Time = 0.53 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{20-19 x}}{\ln \left (-\frac {33 x}{32}+2\right )}\) | \(17\) |
norman | \(\frac {4 \,{\mathrm e}^{20-19 x}}{\ln \left (-\frac {33 x}{32}+2\right )}\) | \(18\) |
parallelrisch | \(\frac {4 \,{\mathrm e}^{20-19 x}}{\ln \left (-\frac {33 x}{32}+2\right )}\) | \(18\) |
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Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=4 \, e^{\left (-19 \, x - \log \left (\log \left (-\frac {33}{32} \, x + 2\right )\right ) + 20\right )} \]
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Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=\frac {4 e^{20 - 19 x}}{\log {\left (2 - \frac {33 x}{32} \right )}} \]
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Time = 0.32 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.29 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=-\frac {4 \, e^{20}}{5 \, e^{\left (19 \, x\right )} \log \left (2\right ) - e^{\left (19 \, x\right )} \log \left (-33 \, x + 64\right )} \]
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Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=-\frac {4 \, e^{\left (-19 \, x + 20\right )}}{5 \, \log \left (2\right ) - \log \left (-33 \, x + 64\right )} \]
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Time = 11.95 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.76 \[ \int \frac {e^{20-19 x} \left (-132+(4864-2508 x) \log \left (\frac {1}{32} (64-33 x)\right )\right )}{(-64+33 x) \log ^2\left (\frac {1}{32} (64-33 x)\right )} \, dx=\frac {4\,{\mathrm {e}}^{-19\,x}\,{\mathrm {e}}^{20}}{\ln \left (2-\frac {33\,x}{32}\right )} \]
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