Optimal. Leaf size=31 \[ x \left (e^3+\frac {1}{2} \left (-1-e^{-3+x}+2 (-5-x)+2 x\right )\right )^2 \]
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Rubi [B] time = 0.08, antiderivative size = 83, normalized size of antiderivative = 2.68, number of steps used = 7, number of rules used = 4, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.082, Rules used = {12, 2176, 2194, 2187} \begin {gather*} \frac {1}{4} \left (11-2 e^3\right )^2 x-\frac {1}{8} e^{2 x-6}+\frac {1}{8} e^{2 x-6} (2 x+1)+\frac {1}{2} e^{x-3} \left (\left (11-2 e^3\right ) x-2 e^3+11\right )-\frac {1}{2} \left (11-2 e^3\right ) e^{x-3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2187
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (121-44 e^3+4 e^6+e^{-6+2 x} (1+2 x)+e^{-3+x} \left (22+e^3 (-4-4 x)+22 x\right )\right ) \, dx\\ &=\frac {1}{4} \left (11-2 e^3\right )^2 x+\frac {1}{4} \int e^{-6+2 x} (1+2 x) \, dx+\frac {1}{4} \int e^{-3+x} \left (22+e^3 (-4-4 x)+22 x\right ) \, dx\\ &=\frac {1}{4} \left (11-2 e^3\right )^2 x+\frac {1}{8} e^{-6+2 x} (1+2 x)-\frac {1}{4} \int e^{-6+2 x} \, dx+\frac {1}{4} \int e^{-3+x} \left (2 \left (11-2 e^3\right )+2 \left (11-2 e^3\right ) x\right ) \, dx\\ &=-\frac {1}{8} e^{-6+2 x}+\frac {1}{4} \left (11-2 e^3\right )^2 x+\frac {1}{8} e^{-6+2 x} (1+2 x)+\frac {1}{2} e^{-3+x} \left (11-2 e^3+\left (11-2 e^3\right ) x\right )+\frac {1}{2} \left (-11+2 e^3\right ) \int e^{-3+x} \, dx\\ &=-\frac {1}{8} e^{-6+2 x}-\frac {1}{2} e^{-3+x} \left (11-2 e^3\right )+\frac {1}{4} \left (11-2 e^3\right )^2 x+\frac {1}{8} e^{-6+2 x} (1+2 x)+\frac {1}{2} e^{-3+x} \left (11-2 e^3+\left (11-2 e^3\right ) x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 24, normalized size = 0.77 \begin {gather*} \frac {\left (11 e^3-2 e^6+e^x\right )^2 x}{4 e^6} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.75, size = 37, normalized size = 1.19 \begin {gather*} x e^{6} - 11 \, x e^{3} + \frac {1}{4} \, x e^{\left (2 \, x - 6\right )} - \frac {1}{2} \, {\left (2 \, x e^{3} - 11 \, x\right )} e^{\left (x - 3\right )} + \frac {121}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 34, normalized size = 1.10 \begin {gather*} x e^{6} - 11 \, x e^{3} + \frac {1}{4} \, x e^{\left (2 \, x - 6\right )} + \frac {11}{2} \, x e^{\left (x - 3\right )} - x e^{x} + \frac {121}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 35, normalized size = 1.13
method | result | size |
norman | \(\left ({\mathrm e}^{6}-11 \,{\mathrm e}^{3}+\frac {121}{4}\right ) x +\left (-{\mathrm e}^{3}+\frac {11}{2}\right ) x \,{\mathrm e}^{x -3}+\frac {x \,{\mathrm e}^{2 x -6}}{4}\) | \(35\) |
risch | \(\frac {x \,{\mathrm e}^{2 x -6}}{4}-\frac {\left (2 \,{\mathrm e}^{3}-11\right ) x \,{\mathrm e}^{x -3}}{2}+x \,{\mathrm e}^{6}-11 x \,{\mathrm e}^{3}+\frac {121 x}{4}\) | \(36\) |
default | \(\frac {121 x}{4}+x \,{\mathrm e}^{6}+\frac {3 \,{\mathrm e}^{2 x -6}}{4}+\frac {{\mathrm e}^{2 x -6} \left (x -3\right )}{4}+\frac {11 \,{\mathrm e}^{x -3} \left (x -3\right )}{2}+\frac {33 \,{\mathrm e}^{x -3}}{2}-4 \,{\mathrm e}^{3} {\mathrm e}^{x -3}-{\mathrm e}^{3} \left ({\mathrm e}^{x -3} \left (x -3\right )-{\mathrm e}^{x -3}\right )-11 x \,{\mathrm e}^{3}\) | \(77\) |
derivativedivides | \(\frac {121 x}{4}-\frac {363}{4}+{\mathrm e}^{6} \left (x -3\right )+\frac {3 \,{\mathrm e}^{2 x -6}}{4}+\frac {{\mathrm e}^{2 x -6} \left (x -3\right )}{4}+\frac {11 \,{\mathrm e}^{x -3} \left (x -3\right )}{2}+\frac {33 \,{\mathrm e}^{x -3}}{2}-4 \,{\mathrm e}^{3} {\mathrm e}^{x -3}-{\mathrm e}^{3} \left ({\mathrm e}^{x -3} \left (x -3\right )-{\mathrm e}^{x -3}\right )-11 \,{\mathrm e}^{3} \left (x -3\right )\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.46, size = 35, normalized size = 1.13 \begin {gather*} -\frac {1}{2} \, x {\left (2 \, e^{3} - 11\right )} e^{\left (x - 3\right )} + x e^{6} - 11 \, x e^{3} + \frac {1}{4} \, x e^{\left (2 \, x - 6\right )} + \frac {121}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.36, size = 15, normalized size = 0.48 \begin {gather*} \frac {x\,{\left ({\mathrm {e}}^{x-3}-2\,{\mathrm {e}}^3+11\right )}^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.15, size = 39, normalized size = 1.26 \begin {gather*} \frac {x e^{2 x - 6}}{4} + x \left (- 11 e^{3} + \frac {121}{4} + e^{6}\right ) + \frac {\left (- 8 x e^{3} + 44 x\right ) e^{x - 3}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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