Optimal. Leaf size=29 \[ (1+5 x) \left (4+\frac {10 \left (-e^{\frac {16}{\left (-4+x+x^2\right )^2}}+x\right )}{x^2}\right ) \]
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Rubi [F] time = 5.02, 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 {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10 \left (x \left (-1+2 x^2\right )+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{\left (-4+x+x^2\right )^3}\right )}{x^3} \, dx\\ &=10 \int \frac {x \left (-1+2 x^2\right )+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{\left (-4+x+x^2\right )^3}}{x^3} \, dx\\ &=10 \int \left (\frac {-1+2 x^2}{x^2}+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{x^3 \left (-4+x+x^2\right )^3}\right ) \, dx\\ &=10 \int \frac {-1+2 x^2}{x^2} \, dx+10 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{x^3 \left (-4+x+x^2\right )^3} \, dx\\ &=10 \int \left (2-\frac {1}{x^2}\right ) \, dx+10 \int \left (\frac {2 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3}+\frac {9 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{2 x^2}-\frac {31 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{8 x}+\frac {2 e^{\frac {16}{\left (-4+x+x^2\right )^2}} (193+29 x)}{\left (-4+x+x^2\right )^3}+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (-17-15 x)}{\left (-4+x+x^2\right )^2}+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (35+31 x)}{8 \left (-4+x+x^2\right )}\right ) \, dx\\ &=\frac {10}{x}+20 x+\frac {5}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (35+31 x)}{-4+x+x^2} \, dx+10 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (-17-15 x)}{\left (-4+x+x^2\right )^2} \, dx+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (193+29 x)}{\left (-4+x+x^2\right )^3} \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx\\ &=\frac {10}{x}+20 x+\frac {5}{4} \int \left (\frac {\left (31+\frac {39}{\sqrt {17}}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1-\sqrt {17}+2 x}+\frac {\left (31-\frac {39}{\sqrt {17}}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x}\right ) \, dx+10 \int \left (-\frac {17 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^2}-\frac {15 e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^2}\right ) \, dx+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx+20 \int \left (\frac {193 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^3}+\frac {29 e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^3}\right ) \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx\\ &=\frac {10}{x}+20 x+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx-150 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^2} \, dx-170 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^2} \, dx+580 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^3} \, dx+3860 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^3} \, dx+\frac {1}{68} \left (5 \left (527-39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx+\frac {1}{68} \left (5 \left (527+39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1-\sqrt {17}+2 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.88, size = 33, normalized size = 1.14 \begin {gather*} 10 \left (e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-\frac {1}{x^2}-\frac {5}{x}\right )+\frac {1}{x}+2 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 42, normalized size = 1.45 \begin {gather*} \frac {10 \, {\left (2 \, x^{3} - {\left (5 \, x + 1\right )} e^{\left (\frac {16}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16}\right )} + x\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 101, normalized size = 3.48 \begin {gather*} \frac {10 \, {\left (2 \, x^{3} - 5 \, x e^{\left (-\frac {x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16} + 1\right )} + x - e^{\left (-\frac {x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16} + 1\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 31, normalized size = 1.07
method | result | size |
risch | \(20 x +\frac {10}{x}-\frac {10 \left (1+5 x \right ) {\mathrm e}^{\frac {16}{\left (x^{2}+x -4\right )^{2}}}}{x^{2}}\) | \(31\) |
norman | \(\frac {-595 x^{4}-270 x^{3}+105 x^{6}+960 x^{2}+160 x +20 x^{7}-720 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x +470 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{2}+330 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{3}-110 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{4}-50 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{5}-160 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}}}{x^{2} \left (x^{2}+x -4\right )^{2}}\) | \(205\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.55, size = 377, normalized size = 13.00 \begin {gather*} 20 \, x + \frac {10 \, {\left (567 \, x^{4} + 1284 \, x^{3} - 3013 \, x^{2} - 4466 \, x + 4624\right )}}{289 \, {\left (x^{5} + 2 \, x^{4} - 7 \, x^{3} - 8 \, x^{2} + 16 \, x\right )}} - \frac {10 \, {\left (4134 \, x^{3} - 1891 \, x^{2} - 17512 \, x + 17232\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} + \frac {30 \, {\left (924 \, x^{3} - 1793 \, x^{2} - 4696 \, x + 7536\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} + \frac {95 \, {\left (386 \, x^{3} + x^{2} - 1096 \, x + 656\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {30 \, {\left (29 \, x^{3} + 188 \, x^{2} + 9 \, x - 942\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {245 \, {\left (24 \, x^{3} - 253 \, x^{2} - 152 \, x + 496\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {405 \, {\left (14 \, x^{3} + 21 \, x^{2} + 104 \, x - 96\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {820 \, {\left (12 \, x^{3} + 18 \, x^{2} - 76 \, x - 41\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {35 \, {\left (6 \, x^{3} + 9 \, x^{2} - 38 \, x + 124\right )}}{17 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {10 \, {\left (5 \, x + 1\right )} e^{\left (\frac {16}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.42, size = 42, normalized size = 1.45 \begin {gather*} 20\,x+\frac {10}{x}-\frac {{\mathrm {e}}^{\frac {16}{x^4+2\,x^3-7\,x^2-8\,x+16}}\,\left (50\,x+10\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 37, normalized size = 1.28 \begin {gather*} 20 x + \frac {10}{x} + \frac {\left (- 50 x - 10\right ) e^{\frac {16}{x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 16}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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