Optimal. Leaf size=18 \[ 2+e^{2 x}+\left (16-e^{3 x}\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2194} \begin {gather*} e^{2 x}-32 e^{3 x}+e^{6 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{2 x} \, dx+6 \int e^{6 x} \, dx-96 \int e^{3 x} \, dx\\ &=e^{2 x}-32 e^{3 x}+e^{6 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} e^{2 x} \left (1-32 e^x+e^{4 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 15, normalized size = 0.83 \begin {gather*} e^{\left (6 \, x\right )} - 32 \, e^{\left (3 \, x\right )} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.83 \begin {gather*} e^{\left (6 \, x\right )} - 32 \, e^{\left (3 \, x\right )} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.89
method | result | size |
norman | \({\mathrm e}^{6 x}+{\mathrm e}^{2 x}-32 \,{\mathrm e}^{3 x}\) | \(16\) |
risch | \({\mathrm e}^{6 x}+{\mathrm e}^{2 x}-32 \,{\mathrm e}^{3 x}\) | \(16\) |
meijerg | \(30+{\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(17\) |
default | \({\mathrm e}^{6 x}+{\mathrm e}^{2 x}-32 \,{\mathrm e}^{3 x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 15, normalized size = 0.83 \begin {gather*} e^{\left (6 \, x\right )} - 32 \, e^{\left (3 \, x\right )} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 15, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^{4\,x}-32\,{\mathrm {e}}^x+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 = 0.83 \begin {gather*} e^{6 x} - 32 e^{3 x} + e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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