Optimal. Leaf size=25 \[ 4-\frac {5}{x^2}+\log \left (x-4 x^2-9 (-4+x)^8 x^8\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(25)=50\).
time = 1.02, antiderivative size = 59, normalized size of antiderivative = 2.36, number of steps
used = 3, number of rules used = 2, integrand size = 129, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2099, 1601}
\begin {gather*} -\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) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \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 {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(25)=50\).
time = 0.03, size = 59, normalized size = 2.36 \begin {gather*} -\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 {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs.
\(2(25)=50\).
time = 0.09, size = 60, normalized size = 2.40
method | result | size |
default | \(\ln \left (9 x^{15}-288 x^{14}+4032 x^{13}-32256 x^{12}+161280 x^{11}-516096 x^{10}+1032192 x^{9}-1179648 x^{8}+589824 x^{7}+4 x -1\right )+\ln \left (x \right )-\frac {5}{x^{2}}\) | \(60\) |
norman | \(\ln \left (9 x^{15}-288 x^{14}+4032 x^{13}-32256 x^{12}+161280 x^{11}-516096 x^{10}+1032192 x^{9}-1179648 x^{8}+589824 x^{7}+4 x -1\right )+\ln \left (x \right )-\frac {5}{x^{2}}\) | \(60\) |
risch | \(-\frac {5}{x^{2}}+\ln \left (9 x^{16}-288 x^{15}+4032 x^{14}-32256 x^{13}+161280 x^{12}-516096 x^{11}+1032192 x^{10}-1179648 x^{9}+589824 x^{8}+4 x^{2}-x \right )\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 59 vs.
\(2 (25) = 50\).
time = 0.28, size = 59, normalized size = 2.36 \begin {gather*} -\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (25) = 50\).
time = 0.46, size = 65, normalized size = 2.60 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs.
\(2 (24) = 48\).
time = 0.12, size = 58, normalized size = 2.32 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 61 vs.
\(2 (25) = 50\).
time = 0.41, size = 61, normalized size = 2.44 \begin {gather*} -\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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.24, size = 59, normalized size = 2.36 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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