Optimal. Leaf size=19 \[ -x^2+\left (e^{8+x}+x\right )^2+4 \log (2) \]
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Rubi [A]
time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.32, number of steps
used = 4, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2225, 2207}
\begin {gather*} 2 e^{x+8} (x+1)-2 e^{x+8}+e^{2 x+16} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{16+2 x} \, dx+\int e^{8+x} (2+2 x) \, dx\\ &=e^{16+2 x}+2 e^{8+x} (1+x)-2 \int e^{8+x} \, dx\\ &=-2 e^{8+x}+e^{16+2 x}+2 e^{8+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 1.11 \begin {gather*} 2 \left (\frac {1}{2} e^{16+2 x}+e^{8+x} x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 20, normalized size = 1.05
method | result | size |
risch | \(2 x \,{\mathrm e}^{x +8}+{\mathrm e}^{2 x +16}\) | \(15\) |
default | \(2 \,{\mathrm e}^{8} {\mathrm e}^{x} x +{\mathrm e}^{16} {\mathrm e}^{2 x}\) | \(20\) |
norman | \(2 \,{\mathrm e}^{8} {\mathrm e}^{x} x +{\mathrm e}^{16} {\mathrm e}^{2 x}\) | \(20\) |
meijerg | \(-{\mathrm e}^{16} \left (1-{\mathrm e}^{2 x}\right )+2 \,{\mathrm e}^{8} \left (1-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}\right )-2 \,{\mathrm e}^{8} \left (1-{\mathrm e}^{x}\right )\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 26, normalized size = 1.37 \begin {gather*} 2 \, {\left (x e^{8} - e^{8}\right )} e^{x} + e^{\left (2 \, x + 16\right )} + 2 \, e^{\left (x + 8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 14, normalized size = 0.74 \begin {gather*} 2 \, x e^{\left (x + 8\right )} + e^{\left (2 \, x + 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.89 \begin {gather*} 2 x e^{8} e^{x} + e^{16} e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 0.74 \begin {gather*} 2 \, x e^{\left (x + 8\right )} + e^{\left (2 \, x + 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 13, normalized size = 0.68 \begin {gather*} {\mathrm {e}}^{x+8}\,\left (2\,x+{\mathrm {e}}^{x+8}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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