Optimal. Leaf size=15 \[ e^{-20+\frac {1}{e^{67}}-\left (-3+e^2\right ) x} \]
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Rubi [A]
time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.67, number of steps
used = 3, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 2259, 2225}
\begin {gather*} e^{\frac {e^{67} \left (3-e^2\right ) x-20 e^{67}+1}{e^{67}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rule 2259
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (3-e^2\right ) \int e^{\frac {1+e^{67} \left (-20+3 x-e^2 x\right )}{e^{67}}} \, dx\\ &=\left (3-e^2\right ) \int e^{\frac {1-20 e^{67}+e^{67} \left (3-e^2\right ) x}{e^{67}}} \, dx\\ &=e^{\frac {1-20 e^{67}+e^{67} \left (3-e^2\right ) x}{e^{67}}}\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(32\) vs. \(2(15)=30\).
time = 0.03, size = 32, normalized size = 2.13 \begin {gather*} -\frac {e^{-20+\frac {1}{e^{67}}+3 x-e^2 x} \left (-3+e^2\right )}{3-e^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.35, size = 22, normalized size = 1.47
method | result | size |
derivativedivides | \({\mathrm e}^{\left (\left (-{\mathrm e}^{2} x +3 x -20\right ) {\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}}\) | \(22\) |
default | \({\mathrm e}^{\left (\left (-{\mathrm e}^{2} x +3 x -20\right ) {\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}}\) | \(22\) |
norman | \({\mathrm e}^{\left (\left (-{\mathrm e}^{2} x +3 x -20\right ) {\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}}\) | \(22\) |
gosper | \({\mathrm e}^{-\left ({\mathrm e}^{2} {\mathrm e}^{67} x -3 \,{\mathrm e}^{67} x +20 \,{\mathrm e}^{67}-1\right ) {\mathrm e}^{-67}}\) | \(25\) |
risch | \(\frac {{\mathrm e}^{\left (3 \,{\mathrm e}^{67} x -x \,{\mathrm e}^{69}-20 \,{\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}} {\mathrm e}^{2}}{{\mathrm e}^{2}-3}-\frac {3 \,{\mathrm e}^{\left (3 \,{\mathrm e}^{67} x -x \,{\mathrm e}^{69}-20 \,{\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}}}{{\mathrm e}^{2}-3}\) | \(59\) |
meijerg | \(-\frac {{\mathrm e}^{2+\left (-20 \,{\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}} \left (1-{\mathrm e}^{-x \left ({\mathrm e}^{2}-3\right )}\right )}{{\mathrm e}^{2}-3}+\frac {3 \,{\mathrm e}^{\left (-20 \,{\mathrm e}^{67}+1\right ) {\mathrm e}^{-67}} \left (1-{\mathrm e}^{-x \left ({\mathrm e}^{2}-3\right )}\right )}{{\mathrm e}^{2}-3}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 1.27 \begin {gather*} e^{\left (-{\left ({\left (x e^{2} - 3 \, x + 20\right )} e^{67} - 1\right )} e^{\left (-67\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 20, normalized size = 1.33 \begin {gather*} e^{\left (-{\left (x e^{69} - {\left (3 \, x - 20\right )} e^{67} - 1\right )} e^{\left (-67\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 19, normalized size = 1.27 \begin {gather*} e^{\frac {\left (- x e^{2} + 3 x - 20\right ) e^{67} + 1}{e^{67}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 1.27 \begin {gather*} e^{\left (-{\left ({\left (x e^{2} - 3 \, x + 20\right )} e^{67} - 1\right )} e^{\left (-67\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 16, normalized size = 1.07 \begin {gather*} {\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-20}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{-67}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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