Optimal. Leaf size=27 \[ \log \left (\left (-\left (4-\frac {10}{x}+2 x-x^2\right )^2+\log ^2(4)\right )^2\right ) \]
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Rubi [A]
time = 0.13, antiderivative size = 47, normalized size of antiderivative = 1.74, number of steps
used = 5, number of rules used = 3, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6, 2099, 1601}
\begin {gather*} 2 \log \left (x^3-2 x^2-x (4-\log (4))+10\right )+2 \log \left (x^3-2 x^2-x (4+\log (4))+10\right )-4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 1601
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {400-160 x-72 x^3+16 x^4+24 x^5-8 x^6}{-100 x+80 x^2-36 x^4+4 x^5+4 x^6-x^7+x^3 \left (24+\log ^2(4)\right )} \, dx\\ &=\int \left (-\frac {4}{x}+\frac {2 \left (-4-4 x+3 x^2-\log (4)\right )}{10-2 x^2+x^3-x (4+\log (4))}+\frac {-8-8 x+6 x^2+\log (16)}{10-2 x^2+x^3-x (4-\log (4))}\right ) \, dx\\ &=-4 \log (x)+2 \int \frac {-4-4 x+3 x^2-\log (4)}{10-2 x^2+x^3-x (4+\log (4))} \, dx+\int \frac {-8-8 x+6 x^2+\log (16)}{10-2 x^2+x^3-x (4-\log (4))} \, dx\\ &=-4 \log (x)+2 \log \left (10-2 x^2+x^3-x (4-\log (4))\right )+2 \log \left (10-2 x^2+x^3-x (4+\log (4))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 51, normalized size = 1.89 \begin {gather*} 8 \left (-\frac {\log (x)}{2}+\frac {1}{4} \log \left (100-80 x-24 x^2+36 x^3-4 x^4-4 x^5+x^6-x^2 \log ^2(4)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 48, normalized size = 1.78
method | result | size |
risch | \(-4 \ln \left (x \right )+2 \ln \left (100+x^{6}-4 x^{5}-4 x^{4}+36 x^{3}+\left (-4 \ln \left (2\right )^{2}-24\right ) x^{2}-80 x \right )\) | \(44\) |
default | \(2 \ln \left (x^{3}+2 x \ln \left (2\right )-2 x^{2}-4 x +10\right )+2 \ln \left (x^{3}-2 x \ln \left (2\right )-2 x^{2}-4 x +10\right )-4 \ln \left (x \right )\) | \(48\) |
norman | \(-4 \ln \left (x \right )+2 \ln \left (-x^{3}+2 x \ln \left (2\right )+2 x^{2}+4 x -10\right )+2 \ln \left (x^{3}+2 x \ln \left (2\right )-2 x^{2}-4 x +10\right )\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 45, normalized size = 1.67 \begin {gather*} 2 \, \log \left (x^{3} - 2 \, x^{2} - 2 \, x {\left (\log \left (2\right ) + 2\right )} + 10\right ) + 2 \, \log \left (x^{3} - 2 \, x^{2} + 2 \, x {\left (\log \left (2\right ) - 2\right )} + 10\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 45, normalized size = 1.67 \begin {gather*} 2 \, \log \left (x^{6} - 4 \, x^{5} - 4 \, x^{4} - 4 \, x^{2} \log \left (2\right )^{2} + 36 \, x^{3} - 24 \, x^{2} - 80 \, x + 100\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.05, size = 44, normalized size = 1.63 \begin {gather*} - 4 \log {\left (x \right )} + 2 \log {\left (x^{6} - 4 x^{5} - 4 x^{4} + 36 x^{3} + x^{2} \left (-24 - 4 \log {\left (2 \right )}^{2}\right ) - 80 x + 100 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 50, normalized size = 1.85 \begin {gather*} 2 \, \log \left ({\left | x^{3} - 2 \, x^{2} + 2 \, x \log \left (2\right ) - 4 \, x + 10 \right |}\right ) + 2 \, \log \left ({\left | x^{3} - 2 \, x^{2} - 2 \, x \log \left (2\right ) - 4 \, x + 10 \right |}\right ) - 4 \, \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 = 0.21, size = 45, normalized size = 1.67 \begin {gather*} 2\,\ln \left (36\,x^3-4\,x^2\,{\ln \left (2\right )}^2-24\,x^2-80\,x-4\,x^4-4\,x^5+x^6+100\right )-4\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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