Optimal. Leaf size=33 \[ x \left (e^4+\log \left (2-\frac {x}{2+\frac {e^7}{x}}-\frac {(4+x)^2}{x^2}\right )\right ) \]
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Rubi [F] time = 8.22, 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 {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 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 \left (\frac {128 x^2}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {32 x^3}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {2 x^5}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {e^{14} \left (-16 \left (2-e^4\right )-8 \left (1-e^4\right ) x-e^4 x^2\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {2 e^4 x^2 \left (32+16 x-2 x^2+x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {e^7 x \left (-64 \left (2-e^4\right )-32 \left (1-e^4\right ) x-4 e^4 x^2+\left (2+e^4\right ) x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\log \left (\frac {-16 e^7-8 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+2 x^3-x^4}{x^2 \left (e^7+2 x\right )}\right )\right ) \, dx\\ &=2 \int \frac {x^5}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+32 \int \frac {x^3}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+128 \int \frac {x^2}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\left (2 e^4\right ) \int \frac {x^2 \left (32+16 x-2 x^2+x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+e^7 \int \frac {x \left (-64 \left (2-e^4\right )-32 \left (1-e^4\right ) x-4 e^4 x^2+\left (2+e^4\right ) x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+e^{14} \int \frac {-16 \left (2-e^4\right )-8 \left (1-e^4\right ) x-e^4 x^2}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\int \log \left (\frac {-16 e^7-8 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+2 x^3-x^4}{x^2 \left (e^7+2 x\right )}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.27, size = 51, normalized size = 1.55 \begin {gather*} e^4 x+x \log \left (\frac {e^7 \left (-16-8 x+x^2\right )-x \left (32+16 x-2 x^2+x^3\right )}{x^2 \left (e^7+2 x\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 53, normalized size = 1.61 \begin {gather*} x e^{4} + x \log \left (-\frac {x^{4} - 2 \, x^{3} + 16 \, x^{2} - {\left (x^{2} - 8 \, x - 16\right )} e^{7} + 32 \, x}{2 \, x^{3} + x^{2} e^{7}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 2.17, size = 57, normalized size = 1.73 \begin {gather*} x e^{4} + x \log \left (-\frac {x^{4} - 2 \, x^{3} - x^{2} e^{7} + 16 \, x^{2} + 8 \, x e^{7} + 32 \, x + 16 \, e^{7}}{2 \, x^{3} + x^{2} e^{7}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.62, size = 54, normalized size = 1.64
method | result | size |
norman | \(x \,{\mathrm e}^{4}+x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} {\mathrm e}^{7}+2 x^{3}}\right )\) | \(54\) |
risch | \(x \,{\mathrm e}^{4}+x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} {\mathrm e}^{7}+2 x^{3}}\right )\) | \(54\) |
default | \(x \,{\mathrm e}^{4}+\frac {\left (\munderset {\textit {\_R} =\RootOf \left (2 \textit {\_Z}^{5}+\left ({\mathrm e}^{7}-4\right ) \textit {\_Z}^{4}+\left (-4 \,{\mathrm e}^{7}+32\right ) \textit {\_Z}^{3}+\left (32 \,{\mathrm e}^{7}-{\mathrm e}^{14}+64\right ) \textit {\_Z}^{2}+\left (64 \,{\mathrm e}^{7}+8 \,{\mathrm e}^{14}\right ) \textit {\_Z} +16 \,{\mathrm e}^{14}\right )}{\sum }\frac {\left (\left ({\mathrm e}^{7}+4\right ) \textit {\_R}^{4}+4 \left ({\mathrm e}^{7}-16\right ) \textit {\_R}^{3}+\left (-64 \,{\mathrm e}^{7}+{\mathrm e}^{14}-192\right ) \textit {\_R}^{2}+16 \left (-12 \,{\mathrm e}^{7}-{\mathrm e}^{14}\right ) \textit {\_R} -48 \,{\mathrm e}^{14}\right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R}^{3} {\mathrm e}^{7}+5 \textit {\_R}^{4}-6 \textit {\_R}^{2} {\mathrm e}^{7}-8 \textit {\_R}^{3}+32 \textit {\_R} \,{\mathrm e}^{7}-{\mathrm e}^{14} \textit {\_R} +48 \textit {\_R}^{2}+32 \,{\mathrm e}^{7}+4 \,{\mathrm e}^{14}+64 \textit {\_R}}\right )}{2}+x \ln \left (\frac {-x^{4}+x^{2} {\mathrm e}^{7}+2 x^{3}-8 x \,{\mathrm e}^{7}-16 x^{2}-16 \,{\mathrm e}^{7}-32 x}{x^{2} \left ({\mathrm e}^{7}+2 x \right )}\right )+{\mathrm e}^{-28} \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+\left (-{\mathrm e}^{7}+16\right ) \textit {\_Z}^{2}+\left (8 \,{\mathrm e}^{7}+32\right ) \textit {\_Z} +16 \,{\mathrm e}^{7}\right )}{\sum }\frac {\left (\textit {\_R}^{3} {\mathrm e}^{28}+\left (-16 \,{\mathrm e}^{28}+{\mathrm e}^{35}\right ) \textit {\_R}^{2}+12 \left (-4 \,{\mathrm e}^{28}-{\mathrm e}^{35}\right ) \textit {\_R} -32 \,{\mathrm e}^{35}\right ) \ln \left (x -\textit {\_R} \right )}{-16-2 \textit {\_R}^{3}+\textit {\_R} \,{\mathrm e}^{7}+3 \textit {\_R}^{2}-4 \,{\mathrm e}^{7}-16 \textit {\_R}}\right )-\frac {{\mathrm e}^{7} \ln \left ({\mathrm e}^{7}+2 x \right )}{2}+2 \ln \left ({\mathrm e}^{7}+2 x \right )+64 \,{\mathrm e}^{-7} \ln \left ({\mathrm e}^{7}+2 x \right )-2 \,{\mathrm e}^{-14} \ln \left ({\mathrm e}^{7}+2 x \right ) {\mathrm e}^{14}-384 \,{\mathrm e}^{-14} \ln \left ({\mathrm e}^{7}+2 x \right )-64 \,{\mathrm e}^{-21} \ln \left ({\mathrm e}^{7}+2 x \right ) {\mathrm e}^{14}+384 \,{\mathrm e}^{-28} \ln \left ({\mathrm e}^{7}+2 x \right ) {\mathrm e}^{14}\) | \(415\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 53, normalized size = 1.61 \begin {gather*} x e^{4} + x \log \left (-x^{4} + 2 \, x^{3} + x^{2} {\left (e^{7} - 16\right )} - 8 \, x {\left (e^{7} + 4\right )} - 16 \, e^{7}\right ) - x \log \left (2 \, x + e^{7}\right ) - 2 \, x \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.03, size = 52, normalized size = 1.58 \begin {gather*} x\,\left (\ln \left (-\frac {32\,x+{\mathrm {e}}^7\,\left (-x^2+8\,x+16\right )+16\,x^2-2\,x^3+x^4}{2\,x^3+{\mathrm {e}}^7\,x^2}\right )+{\mathrm {e}}^4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.58, size = 48, normalized size = 1.45 \begin {gather*} x \log {\left (\frac {- x^{4} + 2 x^{3} - 16 x^{2} - 32 x + \left (x^{2} - 8 x - 16\right ) e^{7}}{2 x^{3} + x^{2} e^{7}} \right )} + x e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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