Optimal. Leaf size=28 \[ x^2+e^{\left (e^5+x-x^2\right )^4} (4+2 x)+x \log (4) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(262\) vs. \(2(28)=56\).
time = 3.17, antiderivative size = 262, normalized size of antiderivative = 9.36, number of steps
used = 2, number of rules used = 1, integrand size = 191, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {2326}
\begin {gather*} \frac {2 \left (2 x^8-3 x^7-5 x^6+13 x^5-9 x^4+2 x^3+e^{15} \left (-2 x^2-3 x+2\right )+3 e^{10} \left (2 x^4+x^3-5 x^2+2 x\right )+3 e^5 \left (-2 x^6+x^5+6 x^4-7 x^3+2 x^2\right )\right ) \exp \left (x^8-4 x^7+6 x^6-4 x^5+x^4+4 e^{15} \left (x-x^2\right )+6 e^{10} \left (x^4-2 x^3+x^2\right )+4 e^5 \left (-x^6+3 x^5-3 x^4+x^3\right )+e^{20}\right )}{2 x^7-7 x^6+9 x^5-5 x^4+x^3+3 e^{10} \left (2 x^3-3 x^2+x\right )+3 e^5 \left (-2 x^5+5 x^4-4 x^3+x^2\right )+e^{15} (1-2 x)}+x^2+x \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x^2+x \log (4)+\int \exp \left (e^{20}+x^4-4 x^5+6 x^6-4 x^7+x^8+e^{15} \left (4 x-4 x^2\right )+e^{10} \left (6 x^2-12 x^3+6 x^4\right )+e^5 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )\right ) \left (2+16 x^3-72 x^4+104 x^5-40 x^6-24 x^7+16 x^8+e^{15} \left (16-24 x-16 x^2\right )+e^{10} \left (48 x-120 x^2+24 x^3+48 x^4\right )+e^5 \left (48 x^2-168 x^3+144 x^4+24 x^5-48 x^6\right )\right ) \, dx\\ &=x^2+\frac {2 \exp \left (e^{20}+x^4-4 x^5+6 x^6-4 x^7+x^8+4 e^{15} \left (x-x^2\right )+6 e^{10} \left (x^2-2 x^3+x^4\right )+4 e^5 \left (x^3-3 x^4+3 x^5-x^6\right )\right ) \left (2 x^3-9 x^4+13 x^5-5 x^6-3 x^7+2 x^8+e^{15} \left (2-3 x-2 x^2\right )+3 e^{10} \left (2 x-5 x^2+x^3+2 x^4\right )+3 e^5 \left (2 x^2-7 x^3+6 x^4+x^5-2 x^6\right )\right )}{e^{15} (1-2 x)+x^3-5 x^4+9 x^5-7 x^6+2 x^7+3 e^{10} \left (x-3 x^2+2 x^3\right )+3 e^5 \left (x^2-4 x^3+5 x^4-2 x^5\right )}+x \log (4)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 13.26, size = 26, normalized size = 0.93 \begin {gather*} 2 e^{\left (e^5+x-x^2\right )^4} (2+x)+x (x+\log (4)) \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. \(186\) vs.
\(2(27)=54\).
time = 28.04, size = 187, normalized size = 6.68
method | result | size |
risch | \(\left (2 x +4\right ) {\mathrm e}^{x^{8}-4 x^{6} {\mathrm e}^{5}-4 x^{7}+12 x^{5} {\mathrm e}^{5}+6 x^{6}-12 x^{4} {\mathrm e}^{5}+6 x^{4} {\mathrm e}^{10}-4 x^{5}+4 x^{3} {\mathrm e}^{5}-12 x^{3} {\mathrm e}^{10}+x^{4}+6 \,{\mathrm e}^{10} x^{2}-4 x^{2} {\mathrm e}^{15}+4 x \,{\mathrm e}^{15}+{\mathrm e}^{20}}+2 x \ln \left (2\right )+x^{2}\) | \(102\) |
default | \(2 x \,{\mathrm e}^{{\mathrm e}^{20}+\left (-4 x^{2}+4 x \right ) {\mathrm e}^{15}+\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) {\mathrm e}^{10}+\left (-4 x^{6}+12 x^{5}-12 x^{4}+4 x^{3}\right ) {\mathrm e}^{5}+x^{8}-4 x^{7}+6 x^{6}-4 x^{5}+x^{4}}+4 \,{\mathrm e}^{{\mathrm e}^{20}+\left (-4 x^{2}+4 x \right ) {\mathrm e}^{15}+\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) {\mathrm e}^{10}+\left (-4 x^{6}+12 x^{5}-12 x^{4}+4 x^{3}\right ) {\mathrm e}^{5}+x^{8}-4 x^{7}+6 x^{6}-4 x^{5}+x^{4}}+x^{2}+2 x \ln \left (2\right )\) | \(187\) |
norman | \(2 x \,{\mathrm e}^{{\mathrm e}^{20}+\left (-4 x^{2}+4 x \right ) {\mathrm e}^{15}+\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) {\mathrm e}^{10}+\left (-4 x^{6}+12 x^{5}-12 x^{4}+4 x^{3}\right ) {\mathrm e}^{5}+x^{8}-4 x^{7}+6 x^{6}-4 x^{5}+x^{4}}+4 \,{\mathrm e}^{{\mathrm e}^{20}+\left (-4 x^{2}+4 x \right ) {\mathrm e}^{15}+\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) {\mathrm e}^{10}+\left (-4 x^{6}+12 x^{5}-12 x^{4}+4 x^{3}\right ) {\mathrm e}^{5}+x^{8}-4 x^{7}+6 x^{6}-4 x^{5}+x^{4}}+x^{2}+2 x \ln \left (2\right )\) | \(187\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 106 vs.
\(2 (28) = 56\).
time = 0.40, size = 106, normalized size = 3.79 \begin {gather*} x^{2} + 2 \, {\left (x e^{\left (e^{20}\right )} + 2 \, e^{\left (e^{20}\right )}\right )} e^{\left (x^{8} - 4 \, x^{7} - 4 \, x^{6} e^{5} + 6 \, x^{6} + 12 \, x^{5} e^{5} - 4 \, x^{5} + 6 \, x^{4} e^{10} - 12 \, x^{4} e^{5} + x^{4} - 12 \, x^{3} e^{10} + 4 \, x^{3} e^{5} - 4 \, x^{2} e^{15} + 6 \, x^{2} e^{10} + 4 \, x e^{15}\right )} + 2 \, x \log \left (2\right ) \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. 89 vs.
\(2 (28) = 56\).
time = 0.38, size = 89, normalized size = 3.18 \begin {gather*} x^{2} + 2 \, {\left (x + 2\right )} e^{\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4} - 4 \, {\left (x^{2} - x\right )} e^{15} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{10} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{5} + e^{20}\right )} + 2 \, x \log \left (2\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. 95 vs.
\(2 (26) = 52\).
time = 0.22, size = 95, normalized size = 3.39 \begin {gather*} x^{2} + 2 x \log {\left (2 \right )} + \left (2 x + 4\right ) e^{x^{8} - 4 x^{7} + 6 x^{6} - 4 x^{5} + x^{4} + \left (- 4 x^{2} + 4 x\right ) e^{15} + \left (6 x^{4} - 12 x^{3} + 6 x^{2}\right ) e^{10} + \left (- 4 x^{6} + 12 x^{5} - 12 x^{4} + 4 x^{3}\right ) e^{5} + e^{20}} \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. 192 vs.
\(2 (28) = 56\).
time = 0.74, size = 192, normalized size = 6.86 \begin {gather*} x^{2} + 2 \, {\left (x e^{\left (x^{8} - 4 \, x^{7} - 4 \, x^{6} e^{5} + 6 \, x^{6} + 12 \, x^{5} e^{5} - 4 \, x^{5} + 6 \, x^{4} e^{10} - 12 \, x^{4} e^{5} + x^{4} - 12 \, x^{3} e^{10} + 4 \, x^{3} e^{5} - 4 \, x^{2} e^{15} + 6 \, x^{2} e^{10} + 4 \, x e^{15} + e^{20} + 5\right )} + 2 \, e^{\left (x^{8} - 4 \, x^{7} - 4 \, x^{6} e^{5} + 6 \, x^{6} + 12 \, x^{5} e^{5} - 4 \, x^{5} + 6 \, x^{4} e^{10} - 12 \, x^{4} e^{5} + x^{4} - 12 \, x^{3} e^{10} + 4 \, x^{3} e^{5} - 4 \, x^{2} e^{15} + 6 \, x^{2} e^{10} + 4 \, x e^{15} + e^{20} + 5\right )}\right )} e^{\left (-5\right )} + 2 \, x \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.59, size = 186, normalized size = 6.64 \begin {gather*} 4\,{\mathrm {e}}^{{\mathrm {e}}^{20}+4\,x\,{\mathrm {e}}^{15}+4\,x^3\,{\mathrm {e}}^5-12\,x^4\,{\mathrm {e}}^5+12\,x^5\,{\mathrm {e}}^5-4\,x^6\,{\mathrm {e}}^5+6\,x^2\,{\mathrm {e}}^{10}-12\,x^3\,{\mathrm {e}}^{10}+6\,x^4\,{\mathrm {e}}^{10}-4\,x^2\,{\mathrm {e}}^{15}+x^4-4\,x^5+6\,x^6-4\,x^7+x^8}+2\,x\,\ln \left (2\right )+2\,x\,{\mathrm {e}}^{{\mathrm {e}}^{20}+4\,x\,{\mathrm {e}}^{15}+4\,x^3\,{\mathrm {e}}^5-12\,x^4\,{\mathrm {e}}^5+12\,x^5\,{\mathrm {e}}^5-4\,x^6\,{\mathrm {e}}^5+6\,x^2\,{\mathrm {e}}^{10}-12\,x^3\,{\mathrm {e}}^{10}+6\,x^4\,{\mathrm {e}}^{10}-4\,x^2\,{\mathrm {e}}^{15}+x^4-4\,x^5+6\,x^6-4\,x^7+x^8}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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