Integrand size = 14, antiderivative size = 20 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \log \left (-1+e^4+\frac {1}{4} \left (-\frac {1}{5}+x\right )-x\right ) \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 31} \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \log \left (15 x-20 e^4+21\right ) \]
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Rule 12
Rule 31
Rubi steps \begin{align*} \text {integral}& = -\left (60 \int \frac {1}{-21+20 e^4-15 x} \, dx\right ) \\ & = 4 \log \left (21-20 e^4+15 x\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \log \left (21-20 e^4+15 x\right ) \]
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Time = 0.67 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.55
method | result | size |
parallelrisch | \(4 \ln \left (-\frac {4 \,{\mathrm e}^{4}}{3}+x +\frac {7}{5}\right )\) | \(11\) |
default | \(4 \ln \left (20 \,{\mathrm e}^{4}-15 x -21\right )\) | \(13\) |
norman | \(4 \ln \left (20 \,{\mathrm e}^{4}-15 x -21\right )\) | \(13\) |
risch | \(4 \ln \left (-20 \,{\mathrm e}^{4}+15 x +21\right )\) | \(13\) |
meijerg | \(-\frac {60 \left (-\frac {4 \,{\mathrm e}^{4}}{3}+\frac {7}{5}\right ) \ln \left (1-\frac {15 x}{20 \,{\mathrm e}^{4}-21}\right )}{20 \,{\mathrm e}^{4}-21}\) | \(31\) |
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Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \, \log \left (15 \, x - 20 \, e^{4} + 21\right ) \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \log {\left (15 x - 20 e^{4} + 21 \right )} \]
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Time = 0.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \, \log \left (15 \, x - 20 \, e^{4} + 21\right ) \]
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Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.65 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4 \, \log \left ({\left | 15 \, x - 20 \, e^{4} + 21 \right |}\right ) \]
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Time = 0.11 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50 \[ \int -\frac {60}{-21+20 e^4-15 x} \, dx=4\,\ln \left (x-\frac {4\,{\mathrm {e}}^4}{3}+\frac {7}{5}\right ) \]
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