Optimal. Leaf size=19 \[ 3+e^{e^{-\frac {1}{e^{16}}+5 e^x+x}}+x \]
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Rubi [F]
time = 0.28, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \left (1+\exp \left (e^{\frac {-1+5 e^{16+x}+e^{16} x}{e^{16}}}+\frac {-1+5 e^{16+x}+e^{16} x}{e^{16}}\right ) \left (1+5 e^x\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int \exp \left (e^{\frac {-1+5 e^{16+x}+e^{16} x}{e^{16}}}+\frac {-1+5 e^{16+x}+e^{16} x}{e^{16}}\right ) \left (1+5 e^x\right ) \, dx\\ &=x+\int e^{-\frac {1}{e^{16}}+5 e^x+e^{-\frac {1}{e^{16}}+5 e^x+x}+x} \left (1+5 e^x\right ) \, dx\\ &=x+\text {Subst}\left (\int e^{-\frac {1}{e^{16}}+5 x+e^{-\frac {1}{e^{16}}+5 x} x} (1+5 x) \, dx,x,e^x\right )\\ &=x+\text {Subst}\left (\int \left (e^{-\frac {1}{e^{16}}+5 x+e^{-\frac {1}{e^{16}}+5 x} x}+5 e^{-\frac {1}{e^{16}}+5 x+e^{-\frac {1}{e^{16}}+5 x} x} x\right ) \, dx,x,e^x\right )\\ &=x+5 \text {Subst}\left (\int e^{-\frac {1}{e^{16}}+5 x+e^{-\frac {1}{e^{16}}+5 x} x} x \, dx,x,e^x\right )+\text {Subst}\left (\int e^{-\frac {1}{e^{16}}+5 x+e^{-\frac {1}{e^{16}}+5 x} x} \, dx,x,e^x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.54, size = 18, normalized size = 0.95 \begin {gather*} e^{e^{-\frac {1}{e^{16}}+5 e^x+x}}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.80, size = 22, normalized size = 1.16
method | result | size |
risch | \(x +{\mathrm e}^{{\mathrm e}^{\left (5 \,{\mathrm e}^{x +16}+x \,{\mathrm e}^{16}-1\right ) {\mathrm e}^{-16}}}\) | \(20\) |
default | \(x +{\mathrm e}^{{\mathrm e}^{\left (5 \,{\mathrm e}^{16} {\mathrm e}^{x}+x \,{\mathrm e}^{16}-1\right ) {\mathrm e}^{-16}}}\) | \(22\) |
norman | \(x +{\mathrm e}^{{\mathrm e}^{\left (5 \,{\mathrm e}^{16} {\mathrm e}^{x}+x \,{\mathrm e}^{16}-1\right ) {\mathrm e}^{-16}}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 14, normalized size = 0.74 \begin {gather*} x + e^{\left (e^{\left (x - e^{\left (-16\right )} + 5 \, e^{x}\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. 71 vs.
\(2 (15) = 30\).
time = 0.35, size = 71, normalized size = 3.74 \begin {gather*} {\left (x e^{\left ({\left (x e^{16} + 5 \, e^{\left (x + 16\right )} - 1\right )} e^{\left (-16\right )}\right )} + e^{\left ({\left (x e^{16} + e^{\left ({\left (x e^{16} + 5 \, e^{\left (x + 16\right )} - 1\right )} e^{\left (-16\right )} + 16\right )} + 5 \, e^{\left (x + 16\right )} - 1\right )} e^{\left (-16\right )}\right )}\right )} e^{\left (-{\left (x e^{16} + 5 \, e^{\left (x + 16\right )} - 1\right )} e^{\left (-16\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 22, normalized size = 1.16 \begin {gather*} x + e^{e^{\frac {x e^{16} + 5 e^{16} e^{x} - 1}{e^{16}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.74 \begin {gather*} x + e^{\left (e^{\left (x - e^{\left (-16\right )} + 5 \, e^{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.15, size = 16, normalized size = 0.84 \begin {gather*} x+{\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^{-16}}\,{\mathrm {e}}^{5\,{\mathrm {e}}^x}\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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