Optimal. Leaf size=26 \[ 4+e^{5 x}-x+e^{2 x} \left (5+2 \left (-1+e^x\right )+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.50, number of steps used = 5, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {2194, 2176} \begin {gather*} -x-\frac {e^{2 x}}{2}+2 e^{3 x}+e^{5 x}+\frac {1}{2} e^{2 x} (2 x+7) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+5 \int e^{5 x} \, dx+6 \int e^{3 x} \, dx+\int e^{2 x} (7+2 x) \, dx\\ &=2 e^{3 x}+e^{5 x}-x+\frac {1}{2} e^{2 x} (7+2 x)-\int e^{2 x} \, dx\\ &=-\frac {e^{2 x}}{2}+2 e^{3 x}+e^{5 x}-x+\frac {1}{2} e^{2 x} (7+2 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 25, normalized size = 0.96 \begin {gather*} 2 e^{3 x}+e^{5 x}-x+e^{2 x} (3+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 22, normalized size = 0.85 \begin {gather*} {\left (x + 3\right )} e^{\left (2 \, x\right )} - x + e^{\left (5 \, x\right )} + 2 \, e^{\left (3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 22, normalized size = 0.85 \begin {gather*} {\left (x + 3\right )} e^{\left (2 \, x\right )} - x + e^{\left (5 \, x\right )} + 2 \, e^{\left (3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 23, normalized size = 0.88
method | result | size |
risch | \({\mathrm e}^{5 x}+2 \,{\mathrm e}^{3 x}+\left (3+x \right ) {\mathrm e}^{2 x}-x\) | \(23\) |
default | \(-x +3 \,{\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{3 x}+{\mathrm e}^{5 x}\) | \(27\) |
norman | \(-x +3 \,{\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{3 x}+{\mathrm e}^{5 x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 31, normalized size = 1.19 \begin {gather*} \frac {1}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} - x + e^{\left (5 \, x\right )} + 2 \, e^{\left (3 \, x\right )} + \frac {7}{2} \, 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 = 26, normalized size = 1.00 \begin {gather*} 3\,{\mathrm {e}}^{2\,x}-x+2\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{5\,x}+x\,{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.77 \begin {gather*} - x + \left (x + 3\right ) e^{2 x} + e^{5 x} + 2 e^{3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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