Optimal. Leaf size=20 \[ \left (x-16 x^4-\frac {4}{x+\log (4) \log (5)}\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(20)=40\).
time = 0.15, antiderivative size = 77, normalized size of antiderivative = 3.85, number of steps
used = 2, number of rules used = 1, integrand size = 141, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {2099}
\begin {gather*} 256 x^8-32 x^5+128 x^3+x^2 (1-128 \log (4) \log (5))+\frac {8 \log (4) \log (5) \left (1+16 \log ^3(4) \log ^3(5)\right )}{x+\log (4) \log (5)}+128 x \log ^2(4) \log ^2(5)+\frac {16}{(x+\log (4) \log (5))^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (384 x^2-160 x^4+2048 x^7+128 \log ^2(4) \log ^2(5)-\frac {32}{(x+\log (4) \log (5))^3}-2 x (-1+128 \log (4) \log (5))-\frac {8 \left (\log (4) \log (5)+16 \log ^4(4) \log ^4(5)\right )}{(x+\log (4) \log (5))^2}\right ) \, dx\\ &=128 x^3-32 x^5+256 x^8+128 x \log ^2(4) \log ^2(5)+x^2 (1-128 \log (4) \log (5))+\frac {16}{(x+\log (4) \log (5))^2}+\frac {8 \log (4) \log (5) \left (1+16 \log ^3(4) \log ^3(5)\right )}{x+\log (4) \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(221\) vs. \(2(20)=40\).
time = 0.07, size = 221, normalized size = 11.05 \begin {gather*} \frac {16-32 x^7+256 x^{10}-64 x^6 \log (4) \log (5)+512 x^9 \log (4) \log (5)+8 \log ^2(4) \log ^2(5)+256 x^8 \log ^2(4) \log ^2(5)-\log ^4(4) \log ^4(5)+512 \log ^5(4) \log ^5(5)-32 \log ^7(4) \log ^7(5)-256 \log ^{10}(4) \log ^{10}(5)+x^4 (1+128 \log (4) \log (5))-32 x^5 \left (-4+\log ^2(4) \log ^2(5)\right )-32 x^2 \log ^3(4) \log ^3(5) \left (-16+\log ^2(4) \log ^2(5)+8 \log ^5(4) \log ^5(5)\right )-2 x \log (4) \log (5) \left (-4+\log ^2(4) \log ^2(5)-512 \log ^3(4) \log ^3(5)+32 \log ^5(4) \log ^5(5)+256 \log ^8(4) \log ^8(5)\right )+x^3 \log (5) \log (16)}{(x+\log (4) \log (5))^2} \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. \(79\) vs.
\(2(21)=42\).
time = 0.14, size = 80, normalized size = 4.00
method | result | size |
default | \(256 x^{8}+512 x \ln \left (2\right )^{2} \ln \left (5\right )^{2}-32 x^{5}-256 x^{2} \ln \left (2\right ) \ln \left (5\right )+128 x^{3}+x^{2}+\frac {16}{\left (2 \ln \left (2\right ) \ln \left (5\right )+x \right )^{2}}+\frac {16 \ln \left (2\right ) \ln \left (5\right ) \left (128 \ln \left (2\right )^{3} \ln \left (5\right )^{3}+1\right )}{2 \ln \left (2\right ) \ln \left (5\right )+x}\) | \(80\) |
risch | \(256 x^{8}+512 x \ln \left (2\right )^{2} \ln \left (5\right )^{2}-32 x^{5}-256 x^{2} \ln \left (2\right ) \ln \left (5\right )+128 x^{3}+x^{2}+\frac {\left (512 \ln \left (5\right )^{4} \ln \left (2\right )^{4}+4 \ln \left (2\right ) \ln \left (5\right )\right ) x +1024 \ln \left (2\right )^{5} \ln \left (5\right )^{5}+8 \ln \left (2\right )^{2} \ln \left (5\right )^{2}+4}{\ln \left (2\right )^{2} \ln \left (5\right )^{2}+x \ln \left (2\right ) \ln \left (5\right )+\frac {x^{2}}{4}}\) | \(105\) |
norman | \(\frac {\left (256 \ln \left (2\right ) \ln \left (5\right )+1\right ) x^{4}+\left (-128 \ln \left (2\right )^{2} \ln \left (5\right )^{2}+128\right ) x^{5}+\left (-16 \ln \left (2\right )^{3} \ln \left (5\right )^{3}+16 \ln \left (2\right ) \ln \left (5\right )\right ) x -32 x^{7}+256 x^{10}+4 \ln \left (5\right ) \ln \left (2\right ) x^{3}-128 \ln \left (5\right ) \ln \left (2\right ) x^{6}+1024 \ln \left (5\right ) \ln \left (2\right ) x^{9}+1024 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{8}+16-16 \ln \left (5\right )^{4} \ln \left (2\right )^{4}+32 \ln \left (2\right )^{2} \ln \left (5\right )^{2}}{\left (2 \ln \left (2\right ) \ln \left (5\right )+x \right )^{2}}\) | \(131\) |
gosper | \(-\frac {-1024 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{8}-1024 \ln \left (5\right ) \ln \left (2\right ) x^{9}-256 x^{10}+128 \ln \left (5\right )^{2} \ln \left (2\right )^{2} x^{5}+16 \ln \left (5\right )^{4} \ln \left (2\right )^{4}+128 \ln \left (5\right ) \ln \left (2\right ) x^{6}+16 \ln \left (5\right )^{3} \ln \left (2\right )^{3} x +32 x^{7}-256 x^{4} \ln \left (5\right ) \ln \left (2\right )-4 \ln \left (5\right ) \ln \left (2\right ) x^{3}-128 x^{5}-32 \ln \left (2\right )^{2} \ln \left (5\right )^{2}-x^{4}-16 x \ln \left (2\right ) \ln \left (5\right )-16}{4 \ln \left (2\right )^{2} \ln \left (5\right )^{2}+4 x \ln \left (2\right ) \ln \left (5\right )+x^{2}}\) | \(148\) |
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. 105 vs.
\(2 (23) = 46\).
time = 0.27, size = 105, normalized size = 5.25 \begin {gather*} 256 \, x^{8} - 32 \, x^{5} + 512 \, x \log \left (5\right )^{2} \log \left (2\right )^{2} - {\left (256 \, \log \left (5\right ) \log \left (2\right ) - 1\right )} x^{2} + 128 \, x^{3} + \frac {16 \, {\left (256 \, \log \left (5\right )^{5} \log \left (2\right )^{5} + 2 \, \log \left (5\right )^{2} \log \left (2\right )^{2} + {\left (128 \, \log \left (5\right )^{4} \log \left (2\right )^{4} + \log \left (5\right ) \log \left (2\right )\right )} x + 1\right )}}{4 \, \log \left (5\right )^{2} \log \left (2\right )^{2} + 4 \, x \log \left (5\right ) \log \left (2\right ) + x^{2}} \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. 131 vs.
\(2 (23) = 46\).
time = 0.35, size = 131, normalized size = 6.55 \begin {gather*} \frac {256 \, x^{10} + 4096 \, \log \left (5\right )^{5} \log \left (2\right )^{5} + 4096 \, x \log \left (5\right )^{4} \log \left (2\right )^{4} + 1024 \, x^{2} \log \left (5\right )^{3} \log \left (2\right )^{3} - 32 \, x^{7} + 128 \, x^{5} + 4 \, {\left (256 \, x^{8} - 32 \, x^{5} + x^{2} + 8\right )} \log \left (5\right )^{2} \log \left (2\right )^{2} + x^{4} + 4 \, {\left (256 \, x^{9} - 32 \, x^{6} + 64 \, x^{4} + x^{3} + 4 \, x\right )} \log \left (5\right ) \log \left (2\right ) + 16}{4 \, \log \left (5\right )^{2} \log \left (2\right )^{2} + 4 \, x \log \left (5\right ) \log \left (2\right ) + 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. 114 vs.
\(2 (19) = 38\).
time = 0.26, size = 114, normalized size = 5.70 \begin {gather*} 256 x^{8} - 32 x^{5} + 128 x^{3} + x^{2} \left (- 256 \log {\left (2 \right )} \log {\left (5 \right )} + 1\right ) + 512 x \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2} + \frac {x \left (16 \log {\left (2 \right )} \log {\left (5 \right )} + 2048 \log {\left (2 \right )}^{4} \log {\left (5 \right )}^{4}\right ) + 16 + 32 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2} + 4096 \log {\left (2 \right )}^{5} \log {\left (5 \right )}^{5}}{x^{2} + 4 x \log {\left (2 \right )} \log {\left (5 \right )} + 4 \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{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. 90 vs.
\(2 (23) = 46\).
time = 0.38, size = 90, normalized size = 4.50 \begin {gather*} 256 \, x^{8} - 32 \, x^{5} + 512 \, x \log \left (5\right )^{2} \log \left (2\right )^{2} - 256 \, x^{2} \log \left (5\right ) \log \left (2\right ) + 128 \, x^{3} + x^{2} + \frac {16 \, {\left (256 \, \log \left (5\right )^{5} \log \left (2\right )^{5} + 128 \, x \log \left (5\right )^{4} \log \left (2\right )^{4} + 2 \, \log \left (5\right )^{2} \log \left (2\right )^{2} + x \log \left (5\right ) \log \left (2\right ) + 1\right )}}{{\left (2 \, \log \left (5\right ) \log \left (2\right ) + x\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.22, size = 135, normalized size = 6.75 \begin {gather*} \frac {x\,\left (16\,\ln \left (2\right )\,\ln \left (5\right )+2048\,{\ln \left (2\right )}^4\,{\ln \left (5\right )}^4\right )+32\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2+4096\,{\ln \left (2\right )}^5\,{\ln \left (5\right )}^5+16}{x^2+4\,\ln \left (2\right )\,\ln \left (5\right )\,x+4\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2}+x\,\left (6\,\ln \left (2\right )\,\ln \left (5\right )\,\left (512\,\ln \left (2\right )\,\ln \left (5\right )-2\right )-4608\,{\ln \left (2\right )}^2\,{\ln \left (5\right )}^2+4\,\ln \left (2\right )\,\ln \left (5\right )\,\left (512\,\ln \left (2\right )\,\ln \left (5\right )+3\right )\right )-x^2\,\left (256\,\ln \left (2\right )\,\ln \left (5\right )-1\right )+128\,x^3-32\,x^5+256\,x^8 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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