Optimal. Leaf size=30 \[ 2+3 \left (e^{e^{e^{2-x}}}+\left (3+\frac {2}{-3+x+x^2}\right )^2\right ) \]
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Rubi [A]
time = 0.56, antiderivative size = 42, normalized size of antiderivative = 1.40, number of steps
used = 7, number of rules used = 5, integrand size = 107, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.047, Rules used = {6820, 2320,
2225, 1674, 643} \begin {gather*} -\frac {36}{-x^2-x+3}+\frac {12}{\left (-x^2-x+3\right )^2}+3 e^{e^{e^{2-x}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 643
Rule 1674
Rule 2225
Rule 2320
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3 e^{2+e^{e^{2-x}}+e^{2-x}-x}-\frac {12 \left (-7-11 x+9 x^2+6 x^3\right )}{\left (-3+x+x^2\right )^3}\right ) \, dx\\ &=-\left (3 \int e^{2+e^{e^{2-x}}+e^{2-x}-x} \, dx\right )-12 \int \frac {-7-11 x+9 x^2+6 x^3}{\left (-3+x+x^2\right )^3} \, dx\\ &=\frac {12}{\left (3-x-x^2\right )^2}+\frac {6}{13} \int \frac {-78-156 x}{\left (-3+x+x^2\right )^2} \, dx+3 \text {Subst}\left (\int e^{2+e^{e^2 x}+e^2 x} \, dx,x,e^{-x}\right )\\ &=\frac {12}{\left (3-x-x^2\right )^2}-\frac {36}{3-x-x^2}+\frac {3 \text {Subst}\left (\int e^{2+x} \, dx,x,e^{e^{2-x}}\right )}{e^2}\\ &=3 e^{e^{e^{2-x}}}+\frac {12}{\left (3-x-x^2\right )^2}-\frac {36}{3-x-x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 34, normalized size = 1.13 \begin {gather*} 3 e^{e^{e^{2-x}}}+\frac {12}{\left (-3+x+x^2\right )^2}+\frac {36}{-3+x+x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 43, normalized size = 1.43
method | result | size |
risch | \(\frac {36 x^{2}+36 x -96}{x^{4}+2 x^{3}-5 x^{2}-6 x +9}+3 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2-x}}}\) | \(43\) |
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. 159 vs.
\(2 (28) = 56\).
time = 0.67, size = 159, normalized size = 5.30 \begin {gather*} -\frac {36 \, {\left (18 \, x^{3} - 142 \, x^{2} - 84 \, x + 207\right )}}{169 \, {\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )}} + \frac {42 \, {\left (12 \, x^{3} + 18 \, x^{2} - 56 \, x - 31\right )}}{169 \, {\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )}} + \frac {54 \, {\left (10 \, x^{3} + 15 \, x^{2} + 66 \, x - 54\right )}}{169 \, {\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )}} - \frac {66 \, {\left (6 \, x^{3} + 9 \, x^{2} - 28 \, x + 69\right )}}{169 \, {\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )}} + 3 \, e^{\left (e^{\left (e^{\left (-x + 2\right )}\right )}\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. 96 vs.
\(2 (28) = 56\).
time = 0.37, size = 96, normalized size = 3.20 \begin {gather*} \frac {3 \, {\left ({\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )} e^{\left ({\left (e^{2} + e^{\left (x + e^{\left (-x + 2\right )}\right )} + 2 \, e^{x}\right )} e^{\left (-x\right )}\right )} + 4 \, {\left (3 \, x^{2} + 3 \, x - 8\right )} e^{\left (e^{\left (-x + 2\right )} + 2\right )}\right )} e^{\left (-e^{\left (-x + 2\right )} - 2\right )}}{x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.25, size = 39, normalized size = 1.30 \begin {gather*} - \frac {- 36 x^{2} - 36 x + 96}{x^{4} + 2 x^{3} - 5 x^{2} - 6 x + 9} + 3 e^{e^{e^{2} e^{- x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.29, size = 31, normalized size = 1.03 \begin {gather*} 3\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-x}\,{\mathrm {e}}^2}}+\frac {36\,x^2+36\,x-96}{{\left (x^2+x-3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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