Optimal. Leaf size=15 \[ 17+e^{e^2 x}+x+\frac {x}{e^3} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2194} \begin {gather*} \left (1+\frac {1}{e^3}\right ) x+e^{e^2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (1+e^3+e^{5+e^2 x}\right ) \, dx}{e^3}\\ &=\left (1+\frac {1}{e^3}\right ) x+\frac {\int e^{5+e^2 x} \, dx}{e^3}\\ &=e^{e^2 x}+\left (1+\frac {1}{e^3}\right ) x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.93 \begin {gather*} e^{e^2 x}+x+\frac {x}{e^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 19, normalized size = 1.27 \begin {gather*} {\left (x e^{5} + x e^{2} + e^{\left (x e^{2} + 5\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 16, normalized size = 1.07 \begin {gather*} {\left (x e^{3} + x + e^{\left (x e^{2} + 3\right )}\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 1.13
method | result | size |
risch | \({\mathrm e}^{-3} x \,{\mathrm e}^{3}+x \,{\mathrm e}^{-3}+{\mathrm e}^{{\mathrm e}^{2} x}\) | \(17\) |
default | \({\mathrm e}^{-3} \left (x +x \,{\mathrm e}^{3}+{\mathrm e}^{3} {\mathrm e}^{{\mathrm e}^{2} x}\right )\) | \(24\) |
norman | \(\left ({\mathrm e}^{\frac {3}{2}} {\mathrm e}^{{\mathrm e}^{2} x}+\left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-\frac {3}{2}} x \right ) {\mathrm e}^{-\frac {3}{2}}\) | \(27\) |
derivativedivides | \({\mathrm e}^{-3} {\mathrm e}^{-2} \left ({\mathrm e}^{{\mathrm e}^{2} x} {\mathrm e}^{5}+\left ({\mathrm e}^{3}+1\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{2} x}\right )\right )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 16, normalized size = 1.07 \begin {gather*} {\left (x e^{3} + x + e^{\left (x e^{2} + 3\right )}\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.73, size = 12, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^2}+x\,\left ({\mathrm {e}}^{-3}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 1.00 \begin {gather*} \frac {x \left (1 + e^{3}\right )}{e^{3}} + e^{x e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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