Optimal. Leaf size=25 \[ \frac {e^x \log ^2\left (\log \left (\frac {x^4}{4+\frac {1}{e^{20}}-x}\right )\right )}{x} \]
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Rubi [F] time = 11.33, 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 {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )-e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{x^2 \left (1+4 e^{20}-e^{20} x\right ) \log \left (-\frac {e^{20} x^4}{-1-4 e^{20}+e^{20} x}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [F] time = 0.24, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.88, size = 27, normalized size = 1.08 \begin {gather*} \frac {e^{x} \log \left (\log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )\right )^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left ({\left (x^{2} - 5 \, x + 4\right )} e^{20} - x + 1\right )} e^{x} \log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right ) \log \left (\log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )\right )^{2} + 2 \, {\left ({\left (3 \, x - 16\right )} e^{20} - 4\right )} e^{x} \log \left (\log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )\right )}{{\left (x^{2} - {\left (x^{3} - 4 \, x^{2}\right )} e^{20}\right )} \log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.32, size = 269, normalized size = 10.76
method | result | size |
risch | \(\frac {{\mathrm e}^{x} \ln \left (20+i \pi +4 \ln \relax (x )-\ln \left (\left (x -4\right ) {\mathrm e}^{20}-1\right )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \left (-\mathrm {csgn}\left (i x^{3}\right )+\mathrm {csgn}\left (i x^{2}\right )\right ) \left (-\mathrm {csgn}\left (i x^{3}\right )+\mathrm {csgn}\left (i x \right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{4}\right ) \left (-\mathrm {csgn}\left (i x^{4}\right )+\mathrm {csgn}\left (i x^{3}\right )\right ) \left (-\mathrm {csgn}\left (i x^{4}\right )+\mathrm {csgn}\left (i x \right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right ) \left (-\mathrm {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )+\mathrm {csgn}\left (i x^{4}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )+\mathrm {csgn}\left (\frac {i}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )\right )}{2}+i \pi \mathrm {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )^{2} \left (\mathrm {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )-1\right )\right )^{2}}{x}\) | \(269\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 29, normalized size = 1.16 \begin {gather*} \frac {e^{x} \log \left (-\log \left (-x e^{20} + 4 \, e^{20} + 1\right ) + 4 \, \log \relax (x) + 20\right )^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\,{\mathrm {e}}^x\,\left ({\mathrm {e}}^{20}\,\left (x^2-5\,x+4\right )-x+1\right )\,{\ln \left (\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\right )}^2+{\mathrm {e}}^x\,\left ({\mathrm {e}}^{20}\,\left (6\,x-32\right )-8\right )\,\ln \left (\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\right )}{\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\,\left ({\mathrm {e}}^{20}\,\left (4\,x^2-x^3\right )+x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.01, size = 26, normalized size = 1.04 \begin {gather*} \frac {e^{x} \log {\left (\log {\left (- \frac {x^{4} e^{20}}{\left (x - 4\right ) e^{20} - 1} \right )} \right )}^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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