Optimal. Leaf size=21 \[ \left (4+e^{5 e^2}\right ) \left (-5+e^x+e^{5+x}\right ) x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(96\) vs. \(2(21)=42\).
time = 0.07, antiderivative size = 96, normalized size of antiderivative = 4.57, number of steps
used = 10, number of rules used = 2, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {2207, 2225}
\begin {gather*} -5 e^{5 e^2} x-20 x-4 e^x-4 e^{x+5}-e^{x+5 e^2}-e^{x+5 \left (1+e^2\right )}+4 e^x (x+1)+4 e^{x+5} (x+1)+e^{x+5 e^2} (x+1)+e^{x+5 \left (1+e^2\right )} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-20 x+e^{5 e^2} \int \left (-5+e^x (1+x)+e^{5+x} (1+x)\right ) \, dx+\int e^x (4+4 x) \, dx+\int e^{5+x} (4+4 x) \, dx\\ &=-20 x-5 e^{5 e^2} x+4 e^x (1+x)+4 e^{5+x} (1+x)-4 \int e^x \, dx-4 \int e^{5+x} \, dx+e^{5 e^2} \int e^x (1+x) \, dx+e^{5 e^2} \int e^{5+x} (1+x) \, dx\\ &=-4 e^x-4 e^{5+x}-20 x-5 e^{5 e^2} x+4 e^x (1+x)+4 e^{5+x} (1+x)+e^{5 e^2+x} (1+x)+e^{5 \left (1+e^2\right )+x} (1+x)-e^{5 e^2} \int e^x \, dx-e^{5 e^2} \int e^{5+x} \, dx\\ &=-4 e^x-4 e^{5+x}-e^{5 e^2+x}-e^{5 \left (1+e^2\right )+x}-20 x-5 e^{5 e^2} x+4 e^x (1+x)+4 e^{5+x} (1+x)+e^{5 e^2+x} (1+x)+e^{5 \left (1+e^2\right )+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 26, normalized size = 1.24 \begin {gather*} \left (4+e^{5 e^2}\right ) \left (-5 x+e^x x+e^{5+x} x\right ) \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. \(55\) vs.
\(2(18)=36\).
time = 0.14, size = 56, normalized size = 2.67
method | result | size |
norman | \(\left (-5 \,{\mathrm e}^{5 \,{\mathrm e}^{2}}-20\right ) x +\left ({\mathrm e}^{5} {\mathrm e}^{5 \,{\mathrm e}^{2}}+4 \,{\mathrm e}^{5}+{\mathrm e}^{5 \,{\mathrm e}^{2}}+4\right ) x \,{\mathrm e}^{x}\) | \(36\) |
risch | \(-5 \,{\mathrm e}^{5 \,{\mathrm e}^{2}} x +\left ({\mathrm e}^{5}+1\right ) x \,{\mathrm e}^{5 \,{\mathrm e}^{2}+x}+4 x \,{\mathrm e}^{5+x}+4 \,{\mathrm e}^{x} x -20 x\) | \(38\) |
default | \(-20 x +4 \,{\mathrm e}^{x} x +4 \,{\mathrm e}^{5+x} \left (5+x \right )-20 \,{\mathrm e}^{5+x}+{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{2+\ln \left (5\right )}} x +{\mathrm e}^{5+x} {\mathrm e}^{{\mathrm e}^{2+\ln \left (5\right )}} x -5 \,{\mathrm e}^{{\mathrm e}^{2+\ln \left (5\right )}} x\) | \(56\) |
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. 42 vs.
\(2 (18) = 36\).
time = 0.29, size = 42, normalized size = 2.00 \begin {gather*} 4 \, x e^{\left (x + 5\right )} + 4 \, {\left (x - 1\right )} e^{x} + {\left (x e^{\left (x + 5\right )} + x e^{x} - 5 \, x\right )} e^{\left (5 \, e^{2}\right )} - 20 \, x + 4 \, e^{x} \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. 46 vs.
\(2 (18) = 36\).
time = 0.36, size = 46, normalized size = 2.19 \begin {gather*} -{\left (20 \, x e^{5} - 4 \, {\left (x e^{5} + x\right )} e^{\left (x + 5\right )} + {\left (5 \, x e^{5} - {\left (x e^{5} + x\right )} e^{\left (x + 5\right )}\right )} e^{\left (5 \, e^{2}\right )}\right )} e^{\left (-5\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. 46 vs.
\(2 (19) = 38\).
time = 0.06, size = 46, normalized size = 2.19 \begin {gather*} x \left (- 5 e^{5 e^{2}} - 20\right ) + \left (4 x + 4 x e^{5} + x e^{5 e^{2}} + x e^{5} e^{5 e^{2}}\right ) e^{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. 37 vs.
\(2 (18) = 36\).
time = 0.40, size = 37, normalized size = 1.76 \begin {gather*} 4 \, x e^{\left (x + 5\right )} + 4 \, x e^{x} + {\left (x e^{\left (x + 5\right )} + x e^{x} - 5 \, x\right )} e^{\left (e^{\left (\log \left (5\right ) + 2\right )}\right )} - 20 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.53, size = 35, normalized size = 1.67 \begin {gather*} x\,{\mathrm {e}}^x\,\left ({\mathrm {e}}^{5\,{\mathrm {e}}^2}+4\,{\mathrm {e}}^5+{\mathrm {e}}^{5\,{\mathrm {e}}^2+5}+4\right )-x\,\left (5\,{\mathrm {e}}^{5\,{\mathrm {e}}^2}+20\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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