Optimal. Leaf size=16 \[ (5+\log (x)) \log \left (\log \left (x-(2+x)^4\right )\right ) \]
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Rubi [F] time = 2.67, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {155 x+240 x^2+120 x^3+20 x^4+\left (31 x+48 x^2+24 x^3+4 x^4\right ) \log (x)+\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right ) \log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )}{\left (16 x+31 x^2+24 x^3+8 x^4+x^5\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {155 x+240 x^2+120 x^3+20 x^4+\left (31 x+48 x^2+24 x^3+4 x^4\right ) \log (x)+\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right ) \log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )}{x \left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx\\ &=\int \left (\frac {155}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {240 x}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {120 x^2}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {20 x^3}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {\left (31+48 x+24 x^2+4 x^3\right ) \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {\log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )}{x}\right ) \, dx\\ &=20 \int \frac {x^3}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+120 \int \frac {x^2}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+155 \int \frac {1}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+240 \int \frac {x}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+\int \frac {\left (31+48 x+24 x^2+4 x^3\right ) \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+\int \frac {\log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )}{x} \, dx\\ &=20 \int \frac {x^3}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+120 \int \frac {x^2}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+155 \int \frac {1}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+240 \int \frac {x}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+\int \left (\frac {31 \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {48 x \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {24 x^2 \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}+\frac {4 x^3 \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )}\right ) \, dx+\int \frac {\log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )}{x} \, dx\\ &=4 \int \frac {x^3 \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+20 \int \frac {x^3}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+24 \int \frac {x^2 \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+31 \int \frac {\log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+48 \int \frac {x \log (x)}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+120 \int \frac {x^2}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+155 \int \frac {1}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+240 \int \frac {x}{\left (16+31 x+24 x^2+8 x^3+x^4\right ) \log \left (-16-31 x-24 x^2-8 x^3-x^4\right )} \, dx+\int \frac {\log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.07, size = 50, normalized size = 3.12 \begin {gather*} 5 \log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right )+\log (x) \log \left (\log \left (-16-31 x-24 x^2-8 x^3-x^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 27, normalized size = 1.69 \begin {gather*} {\left (\log \relax (x) + 5\right )} \log \left (\log \left (-x^{4} - 8 \, x^{3} - 24 \, x^{2} - 31 \, x - 16\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [C] time = 0.48, size = 52, normalized size = 3.25 \begin {gather*} \log \relax (x) \log \left (\log \left (-x^{4} - 8 \, x^{3} - 24 \, x^{2} - 31 \, x - 16\right )\right ) + 5 \, \log \left (\pi - i \, \log \left (x^{4} + 8 \, x^{3} + 24 \, x^{2} + 31 \, x + 16\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 51, normalized size = 3.19
method | result | size |
risch | \(\ln \relax (x ) \ln \left (\ln \left (-x^{4}-8 x^{3}-24 x^{2}-31 x -16\right )\right )+5 \ln \left (\ln \left (-x^{4}-8 x^{3}-24 x^{2}-31 x -16\right )\right )\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 27, normalized size = 1.69 \begin {gather*} {\left (\log \relax (x) + 5\right )} \log \left (\log \left (-x^{4} - 8 \, x^{3} - 24 \, x^{2} - 31 \, x - 16\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.33, size = 27, normalized size = 1.69 \begin {gather*} \ln \left (\ln \left (-x^4-8\,x^3-24\,x^2-31\,x-16\right )\right )\,\left (\ln \relax (x)+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.20, size = 51, normalized size = 3.19 \begin {gather*} \log {\relax (x )} \log {\left (\log {\left (- x^{4} - 8 x^{3} - 24 x^{2} - 31 x - 16 \right )} \right )} + 5 \log {\left (\log {\left (- x^{4} - 8 x^{3} - 24 x^{2} - 31 x - 16 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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