Optimal. Leaf size=12 \[ 5 \left (2+x+e^{7+x} x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 21, normalized size of antiderivative = 1.75, number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {14, 2176, 2194} \begin {gather*} 5 x-5 e^{x+7}+5 e^{x+7} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5+5 e^{7+x} (1+x)\right ) \, dx\\ &=5 x+5 \int e^{7+x} (1+x) \, dx\\ &=5 x+5 e^{7+x} (1+x)-5 \int e^{7+x} \, dx\\ &=-5 e^{7+x}+5 x+5 e^{7+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} 5 x+5 e^{7+x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 12, normalized size = 1.00 \begin {gather*} 5 \, x + 5 \, e^{\left (x + \log \relax (x) + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 11, normalized size = 0.92 \begin {gather*} 5 \, x e^{\left (x + 7\right )} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 1.00
method | result | size |
risch | \(5 x +5 x \,{\mathrm e}^{x +7}\) | \(12\) |
norman | \(5 x +5 \,{\mathrm e}^{\ln \relax (x )+x +7}\) | \(13\) |
default | \(5 x +5 \,{\mathrm e}^{x +7} \left (x +7\right )-35 \,{\mathrm e}^{x +7}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 23, normalized size = 1.92 \begin {gather*} 5 \, {\left (x e^{7} - e^{7}\right )} e^{x} + 5 \, x + 5 \, e^{\left (x + 7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.22, size = 9, normalized size = 0.75 \begin {gather*} 5\,x\,\left ({\mathrm {e}}^{x+7}+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.83 \begin {gather*} 5 x e^{x + 7} + 5 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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