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 = {2282, 29} \[ x \]
Antiderivative was successfully verified.
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Rule 29
Rule 2282
Rubi steps
\begin {align*} \int \frac {e^x}{\cosh (x)+\sinh (x)} \, dx &=\operatorname {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 \[ x \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {e^x}{\cosh (x)+\sinh (x)} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.78, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.59, size = 1, normalized size = 1.00 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, 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 = 0.43, size = 1, normalized size = 1.00 \[ x \]
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 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.41, size = 10, normalized size = 10.00 \[ \frac {x e^{x}}{\sinh {\relax (x )} + \cosh {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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