Optimal. Leaf size=27 \[ 16+x \left (9+\left (\frac {x}{4}+2 (3-x) (7+\log (5))^2\right )^2\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(110\) vs. \(2(27)=54\).
time = 0.03, antiderivative size = 110, normalized size of antiderivative = 4.07, number of steps
used = 6, number of rules used = 1, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {12}
\begin {gather*} \frac {152881 x^3}{16}+4 x^3 \log ^4(5)+112 x^3 \log ^3(5)+1175 x^3 \log ^2(5)+5474 x^3 \log (5)-57477 x^2-24 x^2 \log ^4(5)-672 x^2 \log ^3(5)-7053 x^2 \log ^2(5)-32886 x^2 \log (5)+86445 x+36 x \log ^4(5)+1008 x \log ^3(5)+10584 x \log ^2(5)+49392 x \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \left (1383120-1839264 x+458643 x^2+\left (790272-1052352 x+262752 x^2\right ) \log (5)+\left (169344-225696 x+56400 x^2\right ) \log ^2(5)+\left (16128-21504 x+5376 x^2\right ) \log ^3(5)+\left (576-768 x+192 x^2\right ) \log ^4(5)\right ) \, dx\\ &=86445 x-57477 x^2+\frac {152881 x^3}{16}+\frac {1}{16} \log (5) \int \left (790272-1052352 x+262752 x^2\right ) \, dx+\frac {1}{16} \log ^2(5) \int \left (169344-225696 x+56400 x^2\right ) \, dx+\frac {1}{16} \log ^3(5) \int \left (16128-21504 x+5376 x^2\right ) \, dx+\frac {1}{16} \log ^4(5) \int \left (576-768 x+192 x^2\right ) \, dx\\ &=86445 x-57477 x^2+\frac {152881 x^3}{16}+49392 x \log (5)-32886 x^2 \log (5)+5474 x^3 \log (5)+10584 x \log ^2(5)-7053 x^2 \log ^2(5)+1175 x^3 \log ^2(5)+1008 x \log ^3(5)-672 x^2 \log ^3(5)+112 x^3 \log ^3(5)+36 x \log ^4(5)-24 x^2 \log ^4(5)+4 x^3 \log ^4(5)\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(72\) vs. \(2(27)=54\).
time = 0.02, size = 72, normalized size = 2.67 \begin {gather*} -3 x^2 (7+\log (5))^2 \left (391+112 \log (5)+8 \log ^2(5)\right )+\frac {1}{16} x^3 \left (391+112 \log (5)+8 \log ^2(5)\right )^2+9 x \left (9605+5488 \log (5)+1176 \log ^2(5)+112 \log ^3(5)+4 \log ^4(5)\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. \(108\) vs.
\(2(24)=48\).
time = 0.06, size = 109, normalized size = 4.04
method | result | size |
norman | \(\left (-24 \ln \left (5\right )^{4}-672 \ln \left (5\right )^{3}-7053 \ln \left (5\right )^{2}-32886 \ln \left (5\right )-57477\right ) x^{2}+\left (4 \ln \left (5\right )^{4}+112 \ln \left (5\right )^{3}+1175 \ln \left (5\right )^{2}+5474 \ln \left (5\right )+\frac {152881}{16}\right ) x^{3}+\left (36 \ln \left (5\right )^{4}+1008 \ln \left (5\right )^{3}+10584 \ln \left (5\right )^{2}+49392 \ln \left (5\right )+86445\right ) x\) | \(84\) |
gosper | \(\frac {x \left (64 \ln \left (5\right )^{4} x^{2}-384 x \ln \left (5\right )^{4}+1792 x^{2} \ln \left (5\right )^{3}+576 \ln \left (5\right )^{4}-10752 \ln \left (5\right )^{3} x +18800 x^{2} \ln \left (5\right )^{2}+16128 \ln \left (5\right )^{3}-112848 x \ln \left (5\right )^{2}+87584 x^{2} \ln \left (5\right )+169344 \ln \left (5\right )^{2}-526176 x \ln \left (5\right )+152881 x^{2}+790272 \ln \left (5\right )-919632 x +1383120\right )}{16}\) | \(96\) |
default | \(4 x^{3} \ln \left (5\right )^{4}-24 \ln \left (5\right )^{4} x^{2}+36 x \ln \left (5\right )^{4}+112 x^{3} \ln \left (5\right )^{3}-672 x^{2} \ln \left (5\right )^{3}+1008 \ln \left (5\right )^{3} x +1175 x^{3} \ln \left (5\right )^{2}-7053 x^{2} \ln \left (5\right )^{2}+10584 x \ln \left (5\right )^{2}+5474 x^{3} \ln \left (5\right )-32886 x^{2} \ln \left (5\right )+49392 x \ln \left (5\right )+\frac {152881 x^{3}}{16}-57477 x^{2}+86445 x\) | \(109\) |
risch | \(4 x^{3} \ln \left (5\right )^{4}-24 \ln \left (5\right )^{4} x^{2}+36 x \ln \left (5\right )^{4}+112 x^{3} \ln \left (5\right )^{3}-672 x^{2} \ln \left (5\right )^{3}+1008 \ln \left (5\right )^{3} x +1175 x^{3} \ln \left (5\right )^{2}-7053 x^{2} \ln \left (5\right )^{2}+10584 x \ln \left (5\right )^{2}+5474 x^{3} \ln \left (5\right )-32886 x^{2} \ln \left (5\right )+49392 x \ln \left (5\right )+\frac {152881 x^{3}}{16}-57477 x^{2}+86445 x\) | \(109\) |
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. 87 vs.
\(2 (24) = 48\).
time = 0.39, size = 87, normalized size = 3.22 \begin {gather*} 4 \, {\left (x^{3} - 6 \, x^{2} + 9 \, x\right )} \log \left (5\right )^{4} + 112 \, {\left (x^{3} - 6 \, x^{2} + 9 \, x\right )} \log \left (5\right )^{3} + \frac {152881}{16} \, x^{3} + {\left (1175 \, x^{3} - 7053 \, x^{2} + 10584 \, x\right )} \log \left (5\right )^{2} - 57477 \, x^{2} + 14 \, {\left (391 \, x^{3} - 2349 \, x^{2} + 3528 \, x\right )} \log \left (5\right ) + 86445 \, x \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. 87 vs.
\(2 (24) = 48\).
time = 0.29, size = 87, normalized size = 3.22 \begin {gather*} 4 \, {\left (x^{3} - 6 \, x^{2} + 9 \, x\right )} \log \left (5\right )^{4} + 112 \, {\left (x^{3} - 6 \, x^{2} + 9 \, x\right )} \log \left (5\right )^{3} + \frac {152881}{16} \, x^{3} + {\left (1175 \, x^{3} - 7053 \, x^{2} + 10584 \, x\right )} \log \left (5\right )^{2} - 57477 \, x^{2} + 14 \, {\left (391 \, x^{3} - 2349 \, x^{2} + 3528 \, x\right )} \log \left (5\right ) + 86445 \, x \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. 92 vs.
\(2 (20) = 40\).
time = 0.02, size = 92, normalized size = 3.41 \begin {gather*} x^{3} \cdot \left (4 \log {\left (5 \right )}^{4} + 112 \log {\left (5 \right )}^{3} + 1175 \log {\left (5 \right )}^{2} + 5474 \log {\left (5 \right )} + \frac {152881}{16}\right ) + x^{2} \left (-57477 - 32886 \log {\left (5 \right )} - 7053 \log {\left (5 \right )}^{2} - 672 \log {\left (5 \right )}^{3} - 24 \log {\left (5 \right )}^{4}\right ) + x \left (36 \log {\left (5 \right )}^{4} + 1008 \log {\left (5 \right )}^{3} + 10584 \log {\left (5 \right )}^{2} + 49392 \log {\left (5 \right )} + 86445\right ) \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. 87 vs.
\(2 (24) = 48\).
time = 0.42, size = 87, normalized size = 3.22 \begin {gather*} 4 \, {\left (x^{3} - 6 \, x^{2} + 9 \, x\right )} \log \left (5\right )^{4} + 112 \, {\left (x^{3} - 6 \, x^{2} + 9 \, x\right )} \log \left (5\right )^{3} + \frac {152881}{16} \, x^{3} + {\left (1175 \, x^{3} - 7053 \, x^{2} + 10584 \, x\right )} \log \left (5\right )^{2} - 57477 \, x^{2} + 14 \, {\left (391 \, x^{3} - 2349 \, x^{2} + 3528 \, x\right )} \log \left (5\right ) + 86445 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 84, normalized size = 3.11 \begin {gather*} \left (5474\,\ln \left (5\right )+1175\,{\ln \left (5\right )}^2+112\,{\ln \left (5\right )}^3+4\,{\ln \left (5\right )}^4+\frac {152881}{16}\right )\,x^3+\left (-32886\,\ln \left (5\right )-7053\,{\ln \left (5\right )}^2-672\,{\ln \left (5\right )}^3-24\,{\ln \left (5\right )}^4-57477\right )\,x^2+\left (49392\,\ln \left (5\right )+10584\,{\ln \left (5\right )}^2+1008\,{\ln \left (5\right )}^3+36\,{\ln \left (5\right )}^4+86445\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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