Optimal. Leaf size=27 \[ x \left (9+x+5 \left (\frac {e^{\frac {(4+x)^2}{x^4}}}{x}+\log (25)\right )\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(141\) vs. \(2(27)=54\).
time = 0.22, antiderivative size = 141, normalized size of antiderivative = 5.22, number of steps
used = 5, number of rules used = 3, integrand size = 130, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6, 14, 2326}
\begin {gather*} x^3+2 x^2 (9+5 \log (25))-\frac {25 e^{\frac {2 (x+4)^2}{x^4}} \left (x^2+12 x+32\right )}{\left (\frac {x+4}{x^4}-\frac {2 (x+4)^2}{x^5}\right ) x^6}-\frac {10 e^{\frac {(x+4)^2}{x^4}} \left (x^3+x^2 (21+10 \log (5))+20 x (7+6 \log (5))+32 (9+5 \log (25))\right )}{\left (\frac {x+4}{x^4}-\frac {2 (x+4)^2}{x^5}\right ) x^5}+x (81+10 (9+5 \log (5)) \log (25)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {36 x^7+3 x^8+e^{\frac {2 \left (16+8 x+x^2\right )}{x^4}} \left (-3200-1200 x-100 x^2-25 x^4\right )+\left (90 x^6+20 x^7\right ) \log (25)+e^{\frac {16+8 x+x^2}{x^4}} \left (-5760 x-2800 x^2-420 x^3-20 x^4+10 x^6+\left (-3200 x-1200 x^2-100 x^3\right ) \log (25)\right )+x^6 \left (81+25 \log ^2(25)\right )}{x^6} \, dx\\ &=\int \left (3 x^2-\frac {25 e^{\frac {2 (4+x)^2}{x^4}} \left (128+48 x+4 x^2+x^4\right )}{x^6}+\frac {10 e^{\frac {(4+x)^2}{x^4}} \left (-2 x^3+x^5-42 x^2 \left (1+\frac {10 \log (5)}{21}\right )-280 x \left (1+\frac {6 \log (5)}{7}\right )-576 \left (1+\frac {5 \log (25)}{9}\right )\right )}{x^5}+36 x \left (1+\frac {5 \log (25)}{9}\right )+81 \left (1+\frac {10}{81} (9+5 \log (5)) \log (25)\right )\right ) \, dx\\ &=x^3+2 x^2 (9+5 \log (25))+x (81+10 (9+5 \log (5)) \log (25))+10 \int \frac {e^{\frac {(4+x)^2}{x^4}} \left (-2 x^3+x^5-42 x^2 \left (1+\frac {10 \log (5)}{21}\right )-280 x \left (1+\frac {6 \log (5)}{7}\right )-576 \left (1+\frac {5 \log (25)}{9}\right )\right )}{x^5} \, dx-25 \int \frac {e^{\frac {2 (4+x)^2}{x^4}} \left (128+48 x+4 x^2+x^4\right )}{x^6} \, dx\\ &=x^3-\frac {25 e^{\frac {2 (4+x)^2}{x^4}} \left (32+12 x+x^2\right )}{x^6 \left (\frac {4+x}{x^4}-\frac {2 (4+x)^2}{x^5}\right )}+2 x^2 (9+5 \log (25))+x (81+10 (9+5 \log (5)) \log (25))-\frac {10 e^{\frac {(4+x)^2}{x^4}} \left (x^3+20 x (7+6 \log (5))+x^2 (21+10 \log (5))+32 (9+5 \log (25))\right )}{x^5 \left (\frac {4+x}{x^4}-\frac {2 (4+x)^2}{x^5}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 29, normalized size = 1.07 \begin {gather*} \frac {\left (5 e^{\frac {(4+x)^2}{x^4}}+x (9+x+5 \log (25))\right )^2}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs.
\(2(26)=52\).
time = 0.71, size = 68, normalized size = 2.52
method | result | size |
risch | \(x^{3}+20 x^{2} \ln \left (5\right )+18 x^{2}+100 x \ln \left (5\right )^{2}+180 x \ln \left (5\right )+81 x +\frac {25 \,{\mathrm e}^{\frac {2 \left (4+x \right )^{2}}{x^{4}}}}{x}+\left (90+100 \ln \left (5\right )+10 x \right ) {\mathrm e}^{\frac {\left (4+x \right )^{2}}{x^{4}}}\) | \(68\) |
norman | \(\frac {x^{8}+\left (20 \ln \left (5\right )+18\right ) x^{7}+\left (100 \ln \left (5\right )^{2}+180 \ln \left (5\right )+81\right ) x^{6}+\left (90+100 \ln \left (5\right )\right ) x^{5} {\mathrm e}^{\frac {x^{2}+8 x +16}{x^{4}}}+10 \,{\mathrm e}^{\frac {x^{2}+8 x +16}{x^{4}}} x^{6}+25 \,{\mathrm e}^{\frac {2 x^{2}+16 x +32}{x^{4}}} x^{4}}{x^{5}}\) | \(96\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \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. 83 vs.
\(2 (26) = 52\).
time = 0.37, size = 83, normalized size = 3.07 \begin {gather*} \frac {x^{4} + 100 \, x^{2} \log \left (5\right )^{2} + 18 \, x^{3} + 81 \, x^{2} + 10 \, {\left (x^{2} + 10 \, x \log \left (5\right ) + 9 \, x\right )} e^{\left (\frac {x^{2} + 8 \, x + 16}{x^{4}}\right )} + 20 \, {\left (x^{3} + 9 \, x^{2}\right )} \log \left (5\right ) + 25 \, e^{\left (\frac {2 \, {\left (x^{2} + 8 \, x + 16\right )}}{x^{4}}\right )}}{x} \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. 75 vs.
\(2 (24) = 48\).
time = 0.12, size = 75, normalized size = 2.78 \begin {gather*} x^{3} + x^{2} \cdot \left (18 + 20 \log {\left (5 \right )}\right ) + x \left (81 + 100 \log {\left (5 \right )}^{2} + 180 \log {\left (5 \right )}\right ) + \frac {\left (10 x^{2} + 90 x + 100 x \log {\left (5 \right )}\right ) e^{\frac {x^{2} + 8 x + 16}{x^{4}}} + 25 e^{\frac {2 \left (x^{2} + 8 x + 16\right )}{x^{4}}}}{x} \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. 109 vs.
\(2 (26) = 52\).
time = 0.40, size = 109, normalized size = 4.04 \begin {gather*} \frac {x^{4} + 20 \, x^{3} \log \left (5\right ) + 100 \, x^{2} \log \left (5\right )^{2} + 18 \, x^{3} + 10 \, x^{2} e^{\left (\frac {x^{2} + 8 \, x + 16}{x^{4}}\right )} + 180 \, x^{2} \log \left (5\right ) + 100 \, x e^{\left (\frac {x^{2} + 8 \, x + 16}{x^{4}}\right )} \log \left (5\right ) + 81 \, x^{2} + 90 \, x e^{\left (\frac {x^{2} + 8 \, x + 16}{x^{4}}\right )} + 25 \, e^{\left (\frac {2 \, {\left (x^{2} + 8 \, x + 16\right )}}{x^{4}}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.47, size = 33, normalized size = 1.22 \begin {gather*} \frac {{\left (9\,x+5\,{\mathrm {e}}^{\frac {x^2+8\,x+16}{x^4}}+10\,x\,\ln \left (5\right )+x^2\right )}^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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