Optimal. Leaf size=9 \[ \frac{e^{6 x}}{6} \]
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Rubi [A] time = 0.0258115, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.087, Rules used = {2282, 30} \[ \frac{e^{6 x}}{6} \]
Antiderivative was successfully verified.
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Rule 2282
Rule 30
Rubi steps
\begin{align*} \int \frac{e^{5 x}+e^{7 x}}{e^{-x}+e^x} \, dx &=\operatorname{Subst}\left (\int x^5 \, dx,x,e^x\right )\\ &=\frac{e^{6 x}}{6}\\ \end{align*}
Mathematica [A] time = 0.0010617, size = 9, normalized size = 1. \[ \frac{e^{6 x}}{6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.023, size = 7, normalized size = 0.8 \begin{align*}{\frac{ \left ({{\rm e}^{x}} \right ) ^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989968, size = 8, normalized size = 0.89 \begin{align*} \frac{1}{6} \, e^{\left (6 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.822916, size = 18, normalized size = 2. \begin{align*} \frac{1}{6} \, e^{\left (6 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116089, size = 5, normalized size = 0.56 \begin{align*} \frac{e^{6 x}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21292, size = 8, normalized size = 0.89 \begin{align*} \frac{1}{6} \, e^{\left (6 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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