Optimal. Leaf size=21 \[ 2 x \left (3+e^{5+e^x+2 x} x^4\right )^2 \]
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Rubi [A]
time = 0.03, antiderivative size = 36, normalized size of antiderivative = 1.71, number of steps
used = 3, number of rules used = 1, integrand size = 80, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2326}
\begin {gather*} 2 e^{4 x+2 e^x+10} x^9+12 e^{2 x+e^x+5} x^5+18 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=18 x+\int e^{e^x} \left (12 e^{5+3 x} x^5+e^{5+2 x} \left (60 x^4+24 x^5\right )\right ) \, dx+\int e^{2 e^x} \left (4 e^{10+5 x} x^9+e^{10+4 x} \left (18 x^8+8 x^9\right )\right ) \, dx\\ &=18 x+12 e^{5+e^x+2 x} x^5+2 e^{10+2 e^x+4 x} x^9\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 1.00 \begin {gather*} 2 x \left (3+e^{5+e^x+2 x} x^4\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 33, normalized size = 1.57
method | result | size |
risch | \(2 x^{9} {\mathrm e}^{4 x +10+2 \,{\mathrm e}^{x}}+12 x^{5} {\mathrm e}^{{\mathrm e}^{x}+5+2 x}+18 x\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 32, normalized size = 1.52 \begin {gather*} 2 \, x^{9} e^{\left (4 \, x + 2 \, e^{x} + 10\right )} + 12 \, x^{5} e^{\left (2 \, x + e^{x} + 5\right )} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 32, normalized size = 1.52 \begin {gather*} 2 \, x^{9} e^{\left (4 \, x + 2 \, e^{x} + 10\right )} + 12 \, x^{5} e^{\left (2 \, x + e^{x} + 5\right )} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 41, normalized size = 1.95 \begin {gather*} 2 x^{9} e^{10} e^{4 x} e^{2 e^{x}} + 12 x^{5} e^{5} e^{2 x} e^{e^{x}} + 18 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 32, normalized size = 1.52 \begin {gather*} 2 \, x^{9} e^{\left (4 \, x + 2 \, e^{x} + 10\right )} + 12 \, x^{5} e^{\left (2 \, x + e^{x} + 5\right )} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.21, size = 34, normalized size = 1.62 \begin {gather*} 18\,x+12\,x^5\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^5+2\,x^9\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{10}\,{\mathrm {e}}^{2\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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