Optimal. Leaf size=29 \[ \frac {x}{5 \left (-1+\frac {x}{e^4 \left (\frac {1}{3} \left (-2+\frac {4}{x}\right )+x\right )}\right )^2} \]
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Rubi [C] time = 0.72, antiderivative size = 483, normalized size of antiderivative = 16.66, number of steps used = 11, number of rules used = 5, integrand size = 153, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2074, 638, 614, 618, 204} \begin {gather*} \frac {8 e^4 \left (9-9 e^4+e^8\right ) \left (3 \left (1-e^4\right ) x+e^4\right )}{15 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (-3 \left (1-e^4\right ) x^2-2 e^4 x+4 e^4\right )}+\frac {4 e^4 \left (2 e^4 \left (45-27 e^4-86 e^8+66 e^{12}\right )-3 \left (54-24 e^4-149 e^8+163 e^{12}-44 e^{16}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (-3 \left (1-e^4\right ) x^2-2 e^4 x+4 e^4\right )}-\frac {16 e^8 \left (2 e^4 \left (72-126 e^4+55 e^8\right )-\left (108-207 e^4+111 e^8-11 e^{12}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (-3 \left (1-e^4\right ) x^2-2 e^4 x+4 e^4\right )^2}+\frac {e^8 x}{5 \left (1-e^4\right )^2}-\frac {4 e^2 \left (54+30 e^4-119 e^8+44 e^{12}\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {11 e^4-12}}\right )}{15 \left (1-e^4\right )^3 \left (11 e^4-12\right )^{3/2}}+\frac {8 e^2 \left (9-9 e^4+e^8\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {11 e^4-12}}\right )}{5 \left (1-e^4\right )^3 \left (11 e^4-12\right )^{3/2}}-\frac {4 e^6 \left (7-4 e^4\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {11 e^4-12}}\right )}{15 \left (1-e^4\right )^3 \sqrt {11 e^4-12}} \end {gather*}
Antiderivative was successfully verified.
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Rule 204
Rule 614
Rule 618
Rule 638
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^8}{5 \left (-1+e^4\right )^2}+\frac {64 e^{12} \left (2 \left (18-24 e^4+7 e^8\right )-\left (45-75 e^4+31 e^8\right ) x\right )}{45 \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^3}+\frac {8 e^8 \left (-2 \left (27+9 e^4-64 e^8+30 e^{12}\right )+3 \left (12-3 e^4-25 e^8+16 e^{12}\right ) x\right )}{45 \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2}+\frac {4 e^8 \left (7-4 e^4\right )}{15 \left (1-e^4\right )^3 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}\right ) \, dx\\ &=\frac {e^8 x}{5 \left (1-e^4\right )^2}+\frac {\left (8 e^8\right ) \int \frac {-2 \left (27+9 e^4-64 e^8+30 e^{12}\right )+3 \left (12-3 e^4-25 e^8+16 e^{12}\right ) x}{\left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2} \, dx}{45 \left (1-e^4\right )^4}+\frac {\left (64 e^{12}\right ) \int \frac {2 \left (18-24 e^4+7 e^8\right )-\left (45-75 e^4+31 e^8\right ) x}{\left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^3} \, dx}{45 \left (1-e^4\right )^4}+\frac {\left (4 e^8 \left (7-4 e^4\right )\right ) \int \frac {1}{4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2} \, dx}{15 \left (1-e^4\right )^3}\\ &=\frac {e^8 x}{5 \left (1-e^4\right )^2}-\frac {16 e^8 \left (2 e^4 \left (72-126 e^4+55 e^8\right )-\left (108-207 e^4+111 e^8-11 e^{12}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2}+\frac {4 e^4 \left (2 e^4 \left (45-27 e^4-86 e^8+66 e^{12}\right )-3 \left (54-24 e^4-149 e^8+163 e^{12}-44 e^{16}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}-\frac {\left (8 e^8 \left (7-4 e^4\right )\right ) \operatorname {Subst}\left (\int \frac {1}{4 e^4 \left (12-11 e^4\right )-x^2} \, dx,x,-2 e^4-6 \left (1-e^4\right ) x\right )}{15 \left (1-e^4\right )^3}+\frac {\left (16 e^8 \left (9-9 e^4+e^8\right )\right ) \int \frac {1}{\left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2} \, dx}{15 \left (1-e^4\right )^4}-\frac {\left (4 e^4 \left (54+30 e^4-119 e^8+44 e^{12}\right )\right ) \int \frac {1}{4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2} \, dx}{15 \left (12-11 e^4\right ) \left (1-e^4\right )^3}\\ &=\frac {e^8 x}{5 \left (1-e^4\right )^2}-\frac {16 e^8 \left (2 e^4 \left (72-126 e^4+55 e^8\right )-\left (108-207 e^4+111 e^8-11 e^{12}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2}+\frac {8 e^4 \left (9-9 e^4+e^8\right ) \left (e^4+3 \left (1-e^4\right ) x\right )}{15 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}+\frac {4 e^4 \left (2 e^4 \left (45-27 e^4-86 e^8+66 e^{12}\right )-3 \left (54-24 e^4-149 e^8+163 e^{12}-44 e^{16}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}-\frac {4 e^6 \left (7-4 e^4\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {-12+11 e^4}}\right )}{15 \left (1-e^4\right )^3 \sqrt {-12+11 e^4}}+\frac {\left (8 e^4 \left (9-9 e^4+e^8\right )\right ) \int \frac {1}{4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2} \, dx}{5 \left (12-11 e^4\right ) \left (1-e^4\right )^3}+\frac {\left (8 e^4 \left (54+30 e^4-119 e^8+44 e^{12}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{4 e^4 \left (12-11 e^4\right )-x^2} \, dx,x,-2 e^4-6 \left (1-e^4\right ) x\right )}{15 \left (12-11 e^4\right ) \left (1-e^4\right )^3}\\ &=\frac {e^8 x}{5 \left (1-e^4\right )^2}-\frac {16 e^8 \left (2 e^4 \left (72-126 e^4+55 e^8\right )-\left (108-207 e^4+111 e^8-11 e^{12}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2}+\frac {8 e^4 \left (9-9 e^4+e^8\right ) \left (e^4+3 \left (1-e^4\right ) x\right )}{15 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}+\frac {4 e^4 \left (2 e^4 \left (45-27 e^4-86 e^8+66 e^{12}\right )-3 \left (54-24 e^4-149 e^8+163 e^{12}-44 e^{16}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}-\frac {4 e^6 \left (7-4 e^4\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {-12+11 e^4}}\right )}{15 \left (1-e^4\right )^3 \sqrt {-12+11 e^4}}-\frac {4 e^2 \left (54+30 e^4-119 e^8+44 e^{12}\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {-12+11 e^4}}\right )}{15 \left (1-e^4\right )^3 \left (-12+11 e^4\right )^{3/2}}-\frac {\left (16 e^4 \left (9-9 e^4+e^8\right )\right ) \operatorname {Subst}\left (\int \frac {1}{4 e^4 \left (12-11 e^4\right )-x^2} \, dx,x,-2 e^4-6 \left (1-e^4\right ) x\right )}{5 \left (12-11 e^4\right ) \left (1-e^4\right )^3}\\ &=\frac {e^8 x}{5 \left (1-e^4\right )^2}-\frac {16 e^8 \left (2 e^4 \left (72-126 e^4+55 e^8\right )-\left (108-207 e^4+111 e^8-11 e^{12}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )^2}+\frac {8 e^4 \left (9-9 e^4+e^8\right ) \left (e^4+3 \left (1-e^4\right ) x\right )}{15 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}+\frac {4 e^4 \left (2 e^4 \left (45-27 e^4-86 e^8+66 e^{12}\right )-3 \left (54-24 e^4-149 e^8+163 e^{12}-44 e^{16}\right ) x\right )}{45 \left (12-11 e^4\right ) \left (1-e^4\right )^4 \left (4 e^4-2 e^4 x-3 \left (1-e^4\right ) x^2\right )}-\frac {4 e^6 \left (7-4 e^4\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {-12+11 e^4}}\right )}{15 \left (1-e^4\right )^3 \sqrt {-12+11 e^4}}+\frac {8 e^2 \left (9-9 e^4+e^8\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {-12+11 e^4}}\right )}{5 \left (1-e^4\right )^3 \left (-12+11 e^4\right )^{3/2}}-\frac {4 e^2 \left (54+30 e^4-119 e^8+44 e^{12}\right ) \tan ^{-1}\left (\frac {e^4 (1-3 x)+3 x}{e^2 \sqrt {-12+11 e^4}}\right )}{15 \left (1-e^4\right )^3 \left (-12+11 e^4\right )^{3/2}}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.08, size = 121, normalized size = 4.17 \begin {gather*} \frac {e^8 \left (3 e^{12} x \left (4-2 x+3 x^2\right )^2-e^8 (4+9 x) \left (4-2 x+3 x^2\right )^2-3 x \left (16-16 x+28 x^2+9 x^4\right )+3 e^4 x \left (48-16 x+68 x^2-12 x^3+27 x^4\right )\right )}{15 \left (-1+e^4\right )^3 \left (-3 x^2+e^4 \left (4-2 x+3 x^2\right )\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.80, size = 235, normalized size = 8.10 \begin {gather*} -\frac {3 \, {\left (9 \, x^{5} - 12 \, x^{4} + 28 \, x^{3} - 16 \, x^{2} + 16 \, x\right )} e^{20} - {\left (81 \, x^{5} - 72 \, x^{4} + 204 \, x^{3} - 32 \, x^{2} + 80 \, x + 64\right )} e^{16} + 3 \, {\left (27 \, x^{5} - 12 \, x^{4} + 68 \, x^{3} - 16 \, x^{2} + 48 \, x\right )} e^{12} - 3 \, {\left (9 \, x^{5} + 28 \, x^{3} - 16 \, x^{2} + 16 \, x\right )} e^{8}}{15 \, {\left (9 \, x^{4} - {\left (9 \, x^{4} - 12 \, x^{3} + 28 \, x^{2} - 16 \, x + 16\right )} e^{20} + 3 \, {\left (15 \, x^{4} - 16 \, x^{3} + 36 \, x^{2} - 16 \, x + 16\right )} e^{16} - 6 \, {\left (15 \, x^{4} - 12 \, x^{3} + 26 \, x^{2} - 8 \, x + 8\right )} e^{12} + 2 \, {\left (45 \, x^{4} - 24 \, x^{3} + 50 \, x^{2} - 8 \, x + 8\right )} e^{8} - 3 \, {\left (15 \, x^{4} - 4 \, x^{3} + 8 \, x^{2}\right )} e^{4}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.42, size = 114, normalized size = 3.93
method | result | size |
norman | \(\frac {\frac {9 x^{5} {\mathrm e}^{8}}{5}+\frac {\left (48 \,{\mathrm e}^{12}-96 \,{\mathrm e}^{8}\right ) {\mathrm e}^{-4} x^{2}}{20}+\frac {\left (64 \,{\mathrm e}^{12}+48 \,{\mathrm e}^{8}\right ) {\mathrm e}^{-4} x^{3}}{20}-\frac {3 \left (16 \,{\mathrm e}^{16}+96 \,{\mathrm e}^{12}-48 \,{\mathrm e}^{8}\right ) {\mathrm e}^{-8} x^{4}}{80}+\frac {16 \,{\mathrm e}^{8}}{5}}{\left (3 x^{2} {\mathrm e}^{4}-2 x \,{\mathrm e}^{4}-3 x^{2}+4 \,{\mathrm e}^{4}\right )^{2}}\) | \(114\) |
gosper | \(\frac {9 x^{5} {\mathrm e}^{8}-3 x^{4} {\mathrm e}^{8}+16 x^{3} {\mathrm e}^{8}-18 x^{4} {\mathrm e}^{4}+12 x^{2} {\mathrm e}^{8}+12 x^{3} {\mathrm e}^{4}+9 x^{4}-24 x^{2} {\mathrm e}^{4}+16 \,{\mathrm e}^{8}}{45 x^{4} {\mathrm e}^{8}-60 x^{3} {\mathrm e}^{8}-90 x^{4} {\mathrm e}^{4}+140 x^{2} {\mathrm e}^{8}+60 x^{3} {\mathrm e}^{4}+45 x^{4}-80 x \,{\mathrm e}^{8}-120 x^{2} {\mathrm e}^{4}+80 \,{\mathrm e}^{8}}\) | \(141\) |
risch | \(\frac {x \,{\mathrm e}^{8}}{5 \,{\mathrm e}^{8}-10 \,{\mathrm e}^{4}+5}+\frac {\left (-\frac {16 \,{\mathrm e}^{12}}{9}+\frac {28 \,{\mathrm e}^{8}}{9}\right ) x^{3}-\frac {16 \,{\mathrm e}^{8} \left ({\mathrm e}^{8}+3 \,{\mathrm e}^{4}-3\right ) x^{2}}{27 \left ({\mathrm e}^{4}-1\right )}-\frac {16 \,{\mathrm e}^{8} \left (2 \,{\mathrm e}^{8}-9 \,{\mathrm e}^{4}+3\right ) x}{27 \left ({\mathrm e}^{4}-1\right )}-\frac {64 \,{\mathrm e}^{16}}{27 \left ({\mathrm e}^{4}-1\right )}}{\left (5 \,{\mathrm e}^{8}-10 \,{\mathrm e}^{4}+5\right ) \left (x^{4} {\mathrm e}^{8}-\frac {4 x^{3} {\mathrm e}^{8}}{3}-2 x^{4} {\mathrm e}^{4}+\frac {28 x^{2} {\mathrm e}^{8}}{9}+\frac {4 x^{3} {\mathrm e}^{4}}{3}+x^{4}-\frac {16 x \,{\mathrm e}^{8}}{9}-\frac {8 x^{2} {\mathrm e}^{4}}{3}+\frac {16 \,{\mathrm e}^{8}}{9}\right )}\) | \(153\) |
default | \(\frac {{\mathrm e}^{8} \left (\frac {\left ({\mathrm e}^{4}-1\right ) x}{3 \,{\mathrm e}^{4}+{\mathrm e}^{12}-3 \,{\mathrm e}^{8}-1}+\frac {2 \left (\munderset {\textit {\_R} =\RootOf \left (\left (81 \,{\mathrm e}^{4}+27 \,{\mathrm e}^{12}-81 \,{\mathrm e}^{8}-27\right ) \textit {\_Z}^{6}+\left (-54 \,{\mathrm e}^{4}-54 \,{\mathrm e}^{12}+108 \,{\mathrm e}^{8}\right ) \textit {\_Z}^{5}+\left (108 \,{\mathrm e}^{4}+144 \,{\mathrm e}^{12}-252 \,{\mathrm e}^{8}\right ) \textit {\_Z}^{4}+\left (-152 \,{\mathrm e}^{12}+144 \,{\mathrm e}^{8}\right ) \textit {\_Z}^{3}+\left (192 \,{\mathrm e}^{12}-144 \,{\mathrm e}^{8}\right ) \textit {\_Z}^{2}-96 \textit {\_Z} \,{\mathrm e}^{12}+64 \,{\mathrm e}^{12}\right )}{\sum }\frac {\left (3 \left (-15 \,{\mathrm e}^{8}+4 \,{\mathrm e}^{12}+18 \,{\mathrm e}^{4}-7\right ) \textit {\_R}^{4}+2 \left (12-17 \,{\mathrm e}^{4}+8 \,{\mathrm e}^{12}-3 \,{\mathrm e}^{8}\right ) \textit {\_R}^{3}+12 \left (-2 \,{\mathrm e}^{12}+5 \,{\mathrm e}^{4}-3\right ) \textit {\_R}^{2}+24 \left ({\mathrm e}^{4}+2 \,{\mathrm e}^{12}-3 \,{\mathrm e}^{8}\right ) \textit {\_R} -16 \,{\mathrm e}^{4}-32 \,{\mathrm e}^{12}+48 \,{\mathrm e}^{8}\right ) \ln \left (x -\textit {\_R} \right )}{27 \,{\mathrm e}^{12} \textit {\_R}^{5}-45 \textit {\_R}^{4} {\mathrm e}^{12}-81 \textit {\_R}^{5} {\mathrm e}^{8}+96 \textit {\_R}^{3} {\mathrm e}^{12}+90 \textit {\_R}^{4} {\mathrm e}^{8}+81 \textit {\_R}^{5} {\mathrm e}^{4}-76 \textit {\_R}^{2} {\mathrm e}^{12}-168 \textit {\_R}^{3} {\mathrm e}^{8}-45 \textit {\_R}^{4} {\mathrm e}^{4}-27 \textit {\_R}^{5}+64 \textit {\_R} \,{\mathrm e}^{12}+72 \textit {\_R}^{2} {\mathrm e}^{8}+72 \textit {\_R}^{3} {\mathrm e}^{4}-16 \,{\mathrm e}^{12}-48 \textit {\_R} \,{\mathrm e}^{8}}\right )}{3 \left (3 \,{\mathrm e}^{4}+{\mathrm e}^{12}-3 \,{\mathrm e}^{8}-1\right )}\right )}{5}\) | \(322\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.41, size = 183, normalized size = 6.31 \begin {gather*} \frac {x e^{8}}{5 \, {\left (e^{8} - 2 \, e^{4} + 1\right )}} - \frac {4 \, {\left (3 \, x^{3} {\left (4 \, e^{16} - 11 \, e^{12} + 7 \, e^{8}\right )} + 4 \, x^{2} {\left (e^{16} + 3 \, e^{12} - 3 \, e^{8}\right )} + 4 \, x {\left (2 \, e^{16} - 9 \, e^{12} + 3 \, e^{8}\right )} + 16 \, e^{16}\right )}}{15 \, {\left (9 \, x^{4} {\left (e^{20} - 5 \, e^{16} + 10 \, e^{12} - 10 \, e^{8} + 5 \, e^{4} - 1\right )} - 12 \, x^{3} {\left (e^{20} - 4 \, e^{16} + 6 \, e^{12} - 4 \, e^{8} + e^{4}\right )} + 4 \, x^{2} {\left (7 \, e^{20} - 27 \, e^{16} + 39 \, e^{12} - 25 \, e^{8} + 6 \, e^{4}\right )} - 16 \, x {\left (e^{20} - 3 \, e^{16} + 3 \, e^{12} - e^{8}\right )} + 16 \, e^{20} - 48 \, e^{16} + 48 \, e^{12} - 16 \, e^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 120, normalized size = 4.14 \begin {gather*} \frac {x\,{\mathrm {e}}^8}{5\,{\left ({\mathrm {e}}^4-1\right )}^2}+\frac {16\,{\mathrm {e}}^8\,\left (9\,x-12\,{\mathrm {e}}^4+10\,{\mathrm {e}}^8-9\,x\,{\mathrm {e}}^4+x\,{\mathrm {e}}^8\right )}{45\,{\left ({\mathrm {e}}^4-1\right )}^4\,{\left (\left (3\,{\mathrm {e}}^4-3\right )\,x^2-2\,{\mathrm {e}}^4\,x+4\,{\mathrm {e}}^4\right )}^2}-\frac {4\,{\mathrm {e}}^8\,\left (21\,x-2\,{\mathrm {e}}^4+12\,{\mathrm {e}}^8-33\,x\,{\mathrm {e}}^4+12\,x\,{\mathrm {e}}^8-12\right )}{45\,{\left ({\mathrm {e}}^4-1\right )}^4\,\left (\left (3\,{\mathrm {e}}^4-3\right )\,x^2-2\,{\mathrm {e}}^4\,x+4\,{\mathrm {e}}^4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 5.23, size = 206, normalized size = 7.10 \begin {gather*} \frac {x e^{8}}{- 10 e^{4} + 5 + 5 e^{8}} + \frac {x^{3} \left (- 48 e^{16} - 84 e^{8} + 132 e^{12}\right ) + x^{2} \left (- 16 e^{16} - 48 e^{12} + 48 e^{8}\right ) + x \left (- 32 e^{16} - 48 e^{8} + 144 e^{12}\right ) - 64 e^{16}}{x^{4} \left (- 675 e^{16} - 1350 e^{8} - 135 + 675 e^{4} + 1350 e^{12} + 135 e^{20}\right ) + x^{3} \left (- 180 e^{20} - 1080 e^{12} - 180 e^{4} + 720 e^{8} + 720 e^{16}\right ) + x^{2} \left (- 1620 e^{16} - 1500 e^{8} + 360 e^{4} + 2340 e^{12} + 420 e^{20}\right ) + x \left (- 240 e^{20} - 720 e^{12} + 240 e^{8} + 720 e^{16}\right ) - 720 e^{16} - 240 e^{8} + 720 e^{12} + 240 e^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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