Optimal. Leaf size=9 \[ \frac {e^{6 x}}{6} \]
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Rubi [A]
time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 = {2320, 30}
\begin {gather*} \frac {e^{6 x}}{6} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2320
Rubi steps
\begin {align*} \int \frac {e^{5 x}+e^{7 x}}{e^{-x}+e^x} \, dx &=\text {Subst}\left (\int x^5 \, dx,x,e^x\right )\\ &=\frac {e^{6 x}}{6}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {e^{6 x}}{6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 7, normalized size = 0.78
method | result | size |
default | \(\frac {{\mathrm e}^{6 x}}{6}\) | \(7\) |
norman | \(\frac {{\mathrm e}^{6 x}}{6}\) | \(7\) |
risch | \(\frac {{\mathrm e}^{6 x}}{6}\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 6, normalized size = 0.67 \begin {gather*} \frac {1}{6} \, e^{\left (6 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 6, normalized size = 0.67 \begin {gather*} \frac {1}{6} \, e^{\left (6 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 5, normalized size = 0.56 \begin {gather*} \frac {e^{6 x}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.19, size = 6, normalized size = 0.67 \begin {gather*} \frac {1}{6} \, e^{\left (6 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 6, normalized size = 0.67 \begin {gather*} \frac {{\mathrm {e}}^{6\,x}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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