Integrand size = 129, antiderivative size = 25 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=4-\frac {5}{x^2}+\log \left (x-4 x^2-9 (-4+x)^8 x^8\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(25)=50\).
Time = 0.64 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.36, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2099, 1601} \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=-\frac {5}{x^2}+\log \left (-9 x^{15}+288 x^{14}-4032 x^{13}+32256 x^{12}-161280 x^{11}+516096 x^{10}-1032192 x^9+1179648 x^8-589824 x^7-4 x+1\right )+\log (x) \]
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Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {10}{x^3}+\frac {1}{x}+\frac {4+4128768 x^6-9437184 x^7+9289728 x^8-5160960 x^9+1774080 x^{10}-387072 x^{11}+52416 x^{12}-4032 x^{13}+135 x^{14}}{-1+4 x+589824 x^7-1179648 x^8+1032192 x^9-516096 x^{10}+161280 x^{11}-32256 x^{12}+4032 x^{13}-288 x^{14}+9 x^{15}}\right ) \, dx \\ & = -\frac {5}{x^2}+\log (x)+\int \frac {4+4128768 x^6-9437184 x^7+9289728 x^8-5160960 x^9+1774080 x^{10}-387072 x^{11}+52416 x^{12}-4032 x^{13}+135 x^{14}}{-1+4 x+589824 x^7-1179648 x^8+1032192 x^9-516096 x^{10}+161280 x^{11}-32256 x^{12}+4032 x^{13}-288 x^{14}+9 x^{15}} \, dx \\ & = -\frac {5}{x^2}+\log (x)+\log \left (1-4 x-589824 x^7+1179648 x^8-1032192 x^9+516096 x^{10}-161280 x^{11}+32256 x^{12}-4032 x^{13}+288 x^{14}-9 x^{15}\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(25)=50\).
Time = 0.06 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.36 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=-\frac {5}{x^2}+\log (x)+\log \left (1-4 x-589824 x^7+1179648 x^8-1032192 x^9+516096 x^{10}-161280 x^{11}+32256 x^{12}-4032 x^{13}+288 x^{14}-9 x^{15}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(25)=50\).
Time = 0.10 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.40
method | result | size |
default | \(\ln \left (x \right )-\frac {5}{x^{2}}+\ln \left (9 x^{15}-288 x^{14}+4032 x^{13}-32256 x^{12}+161280 x^{11}-516096 x^{10}+1032192 x^{9}-1179648 x^{8}+589824 x^{7}+4 x -1\right )\) | \(60\) |
norman | \(\ln \left (x \right )-\frac {5}{x^{2}}+\ln \left (9 x^{15}-288 x^{14}+4032 x^{13}-32256 x^{12}+161280 x^{11}-516096 x^{10}+1032192 x^{9}-1179648 x^{8}+589824 x^{7}+4 x -1\right )\) | \(60\) |
risch | \(-\frac {5}{x^{2}}+\ln \left (9 x^{16}-288 x^{15}+4032 x^{14}-32256 x^{13}+161280 x^{12}-516096 x^{11}+1032192 x^{10}-1179648 x^{9}+589824 x^{8}+4 x^{2}-x \right )\) | \(62\) |
parallelrisch | \(\frac {x^{2} \ln \left (x \right )+\ln \left (x^{15}-32 x^{14}+448 x^{13}-3584 x^{12}+17920 x^{11}-57344 x^{10}+114688 x^{9}-131072 x^{8}+65536 x^{7}+\frac {4}{9} x -\frac {1}{9}\right ) x^{2}-5}{x^{2}}\) | \(66\) |
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.60 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=\frac {x^{2} \log \left (9 \, x^{16} - 288 \, x^{15} + 4032 \, x^{14} - 32256 \, x^{13} + 161280 \, x^{12} - 516096 \, x^{11} + 1032192 \, x^{10} - 1179648 \, x^{9} + 589824 \, x^{8} + 4 \, x^{2} - x\right ) - 5}{x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (24) = 48\).
Time = 0.12 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=\log {\left (9 x^{16} - 288 x^{15} + 4032 x^{14} - 32256 x^{13} + 161280 x^{12} - 516096 x^{11} + 1032192 x^{10} - 1179648 x^{9} + 589824 x^{8} + 4 x^{2} - x \right )} - \frac {5}{x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (25) = 50\).
Time = 0.20 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.36 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=-\frac {5}{x^{2}} + \log \left (9 \, x^{15} - 288 \, x^{14} + 4032 \, x^{13} - 32256 \, x^{12} + 161280 \, x^{11} - 516096 \, x^{10} + 1032192 \, x^{9} - 1179648 \, x^{8} + 589824 \, x^{7} + 4 \, x - 1\right ) + \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (25) = 50\).
Time = 0.28 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.44 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=-\frac {5}{x^{2}} + \log \left ({\left | 9 \, x^{15} - 288 \, x^{14} + 4032 \, x^{13} - 32256 \, x^{12} + 161280 \, x^{11} - 516096 \, x^{10} + 1032192 \, x^{9} - 1179648 \, x^{8} + 589824 \, x^{7} + 4 \, x - 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 0.27 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.36 \[ \int \frac {-10+40 x-x^2+8 x^3+5898240 x^7-11796480 x^8+15040512 x^9-15777792 x^{10}+11934720 x^{11}-5999616 x^{12}+1975680 x^{13}-422208 x^{14}+56538 x^{15}-4320 x^{16}+144 x^{17}}{-x^3+4 x^4+589824 x^{10}-1179648 x^{11}+1032192 x^{12}-516096 x^{13}+161280 x^{14}-32256 x^{15}+4032 x^{16}-288 x^{17}+9 x^{18}} \, dx=\ln \left (x^{16}-32\,x^{15}+448\,x^{14}-3584\,x^{13}+17920\,x^{12}-57344\,x^{11}+114688\,x^{10}-131072\,x^9+65536\,x^8+\frac {4\,x^2}{9}-\frac {x}{9}\right )-\frac {5}{x^2} \]
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