Integrand size = 19, antiderivative size = 18 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {3 \left (257-e^5+e^{16}+x\right )}{10 x} \]
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Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 30} \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {3 \left (257-e^5+e^{16}\right )}{10 x} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = -\left (\frac {1}{10} \left (3 \left (257-e^5+e^{16}\right )\right ) \int \frac {1}{x^2} \, dx\right ) \\ & = \frac {3 \left (257-e^5+e^{16}\right )}{10 x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {3 \left (257-e^5+e^{16}\right )}{10 x} \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78
method | result | size |
gosper | \(-\frac {3 \left (-{\mathrm e}^{16}+{\mathrm e}^{5}-257\right )}{10 x}\) | \(14\) |
norman | \(\frac {\frac {3 \,{\mathrm e}^{16}}{10}-\frac {3 \,{\mathrm e}^{5}}{10}+\frac {771}{10}}{x}\) | \(15\) |
default | \(-\frac {-\frac {3 \,{\mathrm e}^{16}}{10}+\frac {3 \,{\mathrm e}^{5}}{10}-\frac {771}{10}}{x}\) | \(16\) |
parallelrisch | \(-\frac {-\frac {3 \,{\mathrm e}^{16}}{10}+\frac {3 \,{\mathrm e}^{5}}{10}-\frac {771}{10}}{x}\) | \(16\) |
risch | \(\frac {3 \,{\mathrm e}^{16}}{10 x}-\frac {3 \,{\mathrm e}^{5}}{10 x}+\frac {771}{10 x}\) | \(21\) |
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {3 \, {\left (e^{16} - e^{5} + 257\right )}}{10 \, x} \]
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Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=- \frac {- \frac {3 e^{16}}{10} - \frac {771}{10} + \frac {3 e^{5}}{10}}{x} \]
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Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {3 \, {\left (e^{16} - e^{5} + 257\right )}}{10 \, x} \]
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {3 \, {\left (e^{16} - e^{5} + 257\right )}}{10 \, x} \]
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Time = 12.67 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {-771+3 e^5-3 e^{16}}{10 x^2} \, dx=\frac {\frac {3\,{\mathrm {e}}^{16}}{10}-\frac {3\,{\mathrm {e}}^5}{10}+\frac {771}{10}}{x} \]
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