Optimal. Leaf size=1 \[ x \]
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Rubi [A]
time = 0.01, antiderivative size = 1, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2320, 29}
\begin {gather*} x \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2320
Rubi steps
\begin {align*} \int \frac {e^x}{\cosh (x)+\sinh (x)} \, dx &=\text {Subst}\left (\int \frac {1}{x} \, dx,x,e^x\right )\\ &=x\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 2, normalized size = 2.00
method | result | size |
default | \(x\) | \(2\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.26, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 10 vs.
\(2 (0) = 0\).
time = 0.16, size = 10, normalized size = 10.00 \begin {gather*} \frac {x e^{x}}{\sinh {\left (x \right )} + \cosh {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.68, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.29, size = 1, normalized size = 1.00 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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