Integrand size = 15, antiderivative size = 20 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=\frac {2 x^5}{2+\frac {1}{5} \left (e-e^2\right )} \]
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Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 30} \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=\frac {10 x^5}{10+e-e^2} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {50 \int x^4 \, dx}{10+e-e^2} \\ & = \frac {10 x^5}{10+e-e^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=-\frac {10 x^5}{-10-e+e^2} \]
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Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80
method | result | size |
gosper | \(-\frac {10 x^{5}}{{\mathrm e}^{2}-{\mathrm e}-10}\) | \(16\) |
default | \(-\frac {10 x^{5}}{{\mathrm e}^{2}-{\mathrm e}-10}\) | \(16\) |
norman | \(-\frac {10 x^{5}}{{\mathrm e}^{2}-{\mathrm e}-10}\) | \(16\) |
risch | \(-\frac {10 x^{5}}{{\mathrm e}^{2}-{\mathrm e}-10}\) | \(16\) |
parallelrisch | \(-\frac {10 x^{5}}{{\mathrm e}^{2}-{\mathrm e}-10}\) | \(16\) |
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none
Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=-\frac {10 \, x^{5}}{e^{2} - e - 10} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=- \frac {10 x^{5}}{-10 - e + e^{2}} \]
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none
Time = 0.20 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=-\frac {10 \, x^{5}}{e^{2} - e - 10} \]
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none
Time = 0.30 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=-\frac {10 \, x^{5}}{e^{2} - e - 10} \]
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Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int -\frac {50 x^4}{-10-e+e^2} \, dx=\frac {10\,x^5}{\mathrm {e}-{\mathrm {e}}^2+10} \]
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