Optimal. Leaf size=30 \[ e^{-4+4 \left (-x+\frac {9}{\left (-3+\left (3-e^x\right ) x (-5+2 x)\right )^2}\right )} \]
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Rubi [F]
time = 104.38, 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 {\exp \left (\frac {2 \left (-198 x-558 x^2-18 x^3+288 x^4-72 x^5+e^{2 x} \left (-50 x^2-10 x^3+32 x^4-8 x^5\right )+e^x \left (60 x+336 x^2+36 x^3-192 x^4+48 x^5\right )\right )}{9+90 x+189 x^2-180 x^3+36 x^4+e^x \left (-30 x-138 x^2+120 x^3-24 x^4\right )+e^{2 x} \left (25 x^2-20 x^3+4 x^4\right )}\right ) \left (-1188-756 x-7452 x^2-7020 x^3+14904 x^4-6480 x^5+864 x^6+e^x \left (360+612 x+5040 x^2+9180 x^3-15336 x^4+6480 x^5-864 x^6\right )+e^{3 x} \left (500 x^3-600 x^4+240 x^5-32 x^6\right )+e^{2 x} \left (-900 x^2-3780 x^3+5256 x^4-2160 x^5+288 x^6\right )\right )}{27+405 x+1863 x^2+1755 x^3-3726 x^4+1620 x^5-216 x^6+e^{2 x} \left (225 x^2+945 x^3-1314 x^4+540 x^5-72 x^6\right )+e^{3 x} \left (-125 x^3+150 x^4-60 x^5+8 x^6\right )+e^x \left (-135 x-1296 x^2-2295 x^3+3834 x^4-1620 x^5+216 x^6\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 {4 \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-e^{3 x} x^3 (-5+2 x)^3+9 e^{2 x} (5-2 x)^2 x^2 \left (-1-5 x+2 x^2\right )+27 \left (-11-7 x-69 x^2-65 x^3+138 x^4-60 x^5+8 x^6\right )-9 e^x \left (-10-17 x-140 x^2-255 x^3+426 x^4-180 x^5+24 x^6\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^3} \, dx\\ &=4 \int \frac {\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-e^{3 x} x^3 (-5+2 x)^3+9 e^{2 x} (5-2 x)^2 x^2 \left (-1-5 x+2 x^2\right )+27 \left (-11-7 x-69 x^2-65 x^3+138 x^4-60 x^5+8 x^6\right )-9 e^x \left (-10-17 x-140 x^2-255 x^3+426 x^4-180 x^5+24 x^6\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^3} \, dx\\ &=4 \int \left (-\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right )-\frac {18 \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-5-x+2 x^2\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^2}-\frac {54 \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (5+x+23 x^2-20 x^3+4 x^4\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^3}\right ) \, dx\\ &=-\left (4 \int \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \, dx\right )-72 \int \frac {\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-5-x+2 x^2\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^2} \, dx-216 \int \frac {\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (5+x+23 x^2-20 x^3+4 x^4\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.44, size = 31, normalized size = 1.03 \begin {gather*} e^{-4-4 x+\frac {36}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 3.22, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (-32 x^{6}+240 x^{5}-600 x^{4}+500 x^{3}\right ) {\mathrm e}^{3 x}+\left (288 x^{6}-2160 x^{5}+5256 x^{4}-3780 x^{3}-900 x^{2}\right ) {\mathrm e}^{2 x}+\left (-864 x^{6}+6480 x^{5}-15336 x^{4}+9180 x^{3}+5040 x^{2}+612 x +360\right ) {\mathrm e}^{x}+864 x^{6}-6480 x^{5}+14904 x^{4}-7020 x^{3}-7452 x^{2}-756 x -1188\right ) {\mathrm e}^{\frac {2 \left (-8 x^{5}+32 x^{4}-10 x^{3}-50 x^{2}\right ) {\mathrm e}^{2 x}+2 \left (48 x^{5}-192 x^{4}+36 x^{3}+336 x^{2}+60 x \right ) {\mathrm e}^{x}-144 x^{5}+576 x^{4}-36 x^{3}-1116 x^{2}-396 x}{\left (4 x^{4}-20 x^{3}+25 x^{2}\right ) {\mathrm e}^{2 x}+\left (-24 x^{4}+120 x^{3}-138 x^{2}-30 x \right ) {\mathrm e}^{x}+36 x^{4}-180 x^{3}+189 x^{2}+90 x +9}}}{\left (8 x^{6}-60 x^{5}+150 x^{4}-125 x^{3}\right ) {\mathrm e}^{3 x}+\left (-72 x^{6}+540 x^{5}-1314 x^{4}+945 x^{3}+225 x^{2}\right ) {\mathrm e}^{2 x}+\left (216 x^{6}-1620 x^{5}+3834 x^{4}-2295 x^{3}-1296 x^{2}-135 x \right ) {\mathrm e}^{x}-216 x^{6}+1620 x^{5}-3726 x^{4}+1755 x^{3}+1863 x^{2}+405 x +27}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-1)] Timed out
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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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 147 vs.
\(2 (23) = 46\).
time = 0.38, size = 147, normalized size = 4.90 \begin {gather*} e^{\left (-\frac {4 \, {\left (36 \, x^{5} - 144 \, x^{4} + 9 \, x^{3} + 279 \, x^{2} + {\left (4 \, x^{5} - 16 \, x^{4} + 5 \, x^{3} + 25 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (4 \, x^{5} - 16 \, x^{4} + 3 \, x^{3} + 28 \, x^{2} + 5 \, x\right )} e^{x} + 99 \, x\right )}}{36 \, x^{4} - 180 \, x^{3} + 189 \, x^{2} + {\left (4 \, x^{4} - 20 \, x^{3} + 25 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (4 \, x^{4} - 20 \, x^{3} + 23 \, x^{2} + 5 \, x\right )} e^{x} + 90 \, x + 9}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 143 vs.
\(2 (22) = 44\).
time = 5.09, size = 143, normalized size = 4.77 \begin {gather*} e^{\frac {2 \left (- 72 x^{5} + 288 x^{4} - 18 x^{3} - 558 x^{2} - 198 x + \left (- 8 x^{5} + 32 x^{4} - 10 x^{3} - 50 x^{2}\right ) e^{2 x} + \left (48 x^{5} - 192 x^{4} + 36 x^{3} + 336 x^{2} + 60 x\right ) e^{x}\right )}{36 x^{4} - 180 x^{3} + 189 x^{2} + 90 x + \left (4 x^{4} - 20 x^{3} + 25 x^{2}\right ) e^{2 x} + \left (- 24 x^{4} + 120 x^{3} - 138 x^{2} - 30 x\right ) e^{x} + 9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 175 vs.
\(2 (23) = 46\).
time = 21.67, size = 175, normalized size = 5.83 \begin {gather*} e^{\left (-3 \, x - \frac {4 \, x^{5} e^{\left (2 \, x\right )} - 24 \, x^{5} e^{x} + 36 \, x^{5} - 4 \, x^{4} e^{\left (2 \, x\right )} + 24 \, x^{4} e^{x} - 36 \, x^{4} - 55 \, x^{3} e^{\left (2 \, x\right )} + 342 \, x^{3} e^{x} - 531 \, x^{3} + 100 \, x^{2} e^{\left (2 \, x\right )} - 582 \, x^{2} e^{x} + 846 \, x^{2} - 120 \, x e^{x} + 369 \, x}{4 \, x^{4} e^{\left (2 \, x\right )} - 24 \, x^{4} e^{x} + 36 \, x^{4} - 20 \, x^{3} e^{\left (2 \, x\right )} + 120 \, x^{3} e^{x} - 180 \, x^{3} + 25 \, x^{2} e^{\left (2 \, x\right )} - 138 \, x^{2} e^{x} + 189 \, x^{2} - 30 \, x e^{x} + 90 \, x + 9}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 9.00, size = 1157, normalized size = 38.57 \begin {gather*} {\mathrm {e}}^{\frac {72\,x^3\,{\mathrm {e}}^x}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{\frac {96\,x^5\,{\mathrm {e}}^x}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {384\,x^4\,{\mathrm {e}}^x}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{\frac {672\,x^2\,{\mathrm {e}}^x}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {36\,x^3}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {144\,x^5}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{\frac {576\,x^4}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {1116\,x^2}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {16\,x^5\,{\mathrm {e}}^{2\,x}}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {20\,x^3\,{\mathrm {e}}^{2\,x}}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{\frac {64\,x^4\,{\mathrm {e}}^{2\,x}}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {100\,x^2\,{\mathrm {e}}^{2\,x}}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{\frac {120\,x\,{\mathrm {e}}^x}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}}\,{\mathrm {e}}^{-\frac {396\,x}{90\,x-138\,x^2\,{\mathrm {e}}^x+120\,x^3\,{\mathrm {e}}^x-24\,x^4\,{\mathrm {e}}^x+25\,x^2\,{\mathrm {e}}^{2\,x}-20\,x^3\,{\mathrm {e}}^{2\,x}+4\,x^4\,{\mathrm {e}}^{2\,x}-30\,x\,{\mathrm {e}}^x+189\,x^2-180\,x^3+36\,x^4+9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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