Integrand size = 47, antiderivative size = 19 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {18}{5} e^2 x^4 \left (-\frac {1}{x}+x\right )^8 \]
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Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(19)=38\).
Time = 0.02 (sec) , antiderivative size = 79, normalized size of antiderivative = 4.16, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 14} \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {18 e^2 x^{12}}{5}-\frac {144 e^2 x^{10}}{5}+\frac {504 e^2 x^8}{5}-\frac {1008 e^2 x^6}{5}+252 e^2 x^4+\frac {18 e^2}{5 x^4}-\frac {1008 e^2 x^2}{5}-\frac {144 e^2}{5 x^2} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} e^2 \int \frac {-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}}{x^5} \, dx \\ & = \frac {1}{5} e^2 \int \left (-\frac {72}{x^5}+\frac {288}{x^3}-2016 x+5040 x^3-6048 x^5+4032 x^7-1440 x^9+216 x^{11}\right ) \, dx \\ & = \frac {18 e^2}{5 x^4}-\frac {144 e^2}{5 x^2}-\frac {1008 e^2 x^2}{5}+252 e^2 x^4-\frac {1008 e^2 x^6}{5}+\frac {504 e^2 x^8}{5}-\frac {144 e^2 x^{10}}{5}+\frac {18 e^2 x^{12}}{5} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(19)=38\).
Time = 0.01 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.84 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {72}{5} e^2 \left (\frac {1}{4 x^4}-\frac {2}{x^2}-14 x^2+\frac {35 x^4}{2}-14 x^6+7 x^8-2 x^{10}+\frac {x^{12}}{4}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(42\) vs. \(2(16)=32\).
Time = 0.05 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.26
method | result | size |
gosper | \(\frac {18 \,{\mathrm e}^{2} \left (x^{16}-8 x^{14}+28 x^{12}-56 x^{10}+70 x^{8}-56 x^{6}-8 x^{2}+1\right )}{5 x^{4}}\) | \(43\) |
parallelrisch | \(\frac {{\mathrm e}^{2} \left (18 x^{16}-144 x^{14}+504 x^{12}-1008 x^{10}+1260 x^{8}-1008 x^{6}-144 x^{2}+18\right )}{5 x^{4}}\) | \(45\) |
default | \(\frac {72 \,{\mathrm e}^{2} \left (\frac {x^{12}}{4}-2 x^{10}+7 x^{8}-14 x^{6}+\frac {35 x^{4}}{2}-14 x^{2}-\frac {2}{x^{2}}+\frac {1}{4 x^{4}}\right )}{5}\) | \(46\) |
norman | \(\frac {-\frac {144 x^{2} {\mathrm e}^{2}}{5}-\frac {1008 x^{6} {\mathrm e}^{2}}{5}+252 x^{8} {\mathrm e}^{2}-\frac {1008 \,{\mathrm e}^{2} x^{10}}{5}+\frac {504 \,{\mathrm e}^{2} x^{12}}{5}-\frac {144 \,{\mathrm e}^{2} x^{14}}{5}+\frac {18 \,{\mathrm e}^{2} x^{16}}{5}+\frac {18 \,{\mathrm e}^{2}}{5}}{x^{4}}\) | \(59\) |
risch | \(-\frac {1008 x^{6} {\mathrm e}^{2}}{5}+\frac {504 x^{8} {\mathrm e}^{2}}{5}-\frac {1008 x^{2} {\mathrm e}^{2}}{5}+252 x^{4} {\mathrm e}^{2}+\frac {432 \,{\mathrm e}^{2}}{5}+\frac {{\mathrm e}^{2} \left (-144 x^{2}+18\right )}{5 x^{4}}-\frac {144 \,{\mathrm e}^{2} x^{10}}{5}+\frac {18 \,{\mathrm e}^{2} x^{12}}{5}\) | \(62\) |
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Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (16) = 32\).
Time = 0.25 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.21 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {18 \, {\left (x^{16} - 8 \, x^{14} + 28 \, x^{12} - 56 \, x^{10} + 70 \, x^{8} - 56 \, x^{6} - 8 \, x^{2} + 1\right )} e^{2}}{5 \, x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (15) = 30\).
Time = 0.08 (sec) , antiderivative size = 76, normalized size of antiderivative = 4.00 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {18 x^{12} e^{2}}{5} - \frac {144 x^{10} e^{2}}{5} + \frac {504 x^{8} e^{2}}{5} - \frac {1008 x^{6} e^{2}}{5} + 252 x^{4} e^{2} - \frac {1008 x^{2} e^{2}}{5} + \frac {- 144 x^{2} e^{2} + 18 e^{2}}{5 x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (16) = 32\).
Time = 0.20 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.37 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {18}{5} \, {\left (x^{12} - 8 \, x^{10} + 28 \, x^{8} - 56 \, x^{6} + 70 \, x^{4} - 56 \, x^{2} - \frac {8 \, x^{2} - 1}{x^{4}}\right )} e^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 45 vs. \(2 (16) = 32\).
Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.37 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=\frac {18}{5} \, {\left (x^{12} - 8 \, x^{10} + 28 \, x^{8} - 56 \, x^{6} + 70 \, x^{4} - 56 \, x^{2} - \frac {8 \, x^{2} - 1}{x^{4}}\right )} e^{2} \]
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Time = 0.07 (sec) , antiderivative size = 60, normalized size of antiderivative = 3.16 \[ \int \frac {e^2 \left (-72+288 x^2-2016 x^6+5040 x^8-6048 x^{10}+4032 x^{12}-1440 x^{14}+216 x^{16}\right )}{5 x^5} \, dx=252\,x^4\,{\mathrm {e}}^2-\frac {1008\,x^2\,{\mathrm {e}}^2}{5}-\frac {1008\,x^6\,{\mathrm {e}}^2}{5}+\frac {504\,x^8\,{\mathrm {e}}^2}{5}-\frac {144\,x^{10}\,{\mathrm {e}}^2}{5}+\frac {18\,x^{12}\,{\mathrm {e}}^2}{5}+\frac {18\,{\mathrm {e}}^2-144\,x^2\,{\mathrm {e}}^2}{5\,x^4} \]
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