Optimal. Leaf size=13 \[ \frac{e^{(m-1) x}}{m-1} \]
[Out]
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Rubi [A] time = 0.047424, antiderivative size = 19, normalized size of antiderivative = 1.46, number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{e^{-(1-m) x}}{1-m} \]
Antiderivative was successfully verified.
[In] Int[E^(m*x)/(Cosh[x] + Sinh[x]),x]
[Out]
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Rubi in Sympy [A] time = 4.33957, size = 10, normalized size = 0.77 \[ - \frac{e^{x \left (m - 1\right )}}{- m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(m*x)/(cosh(x)+sinh(x)),x)
[Out]
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Mathematica [A] time = 0.0184985, size = 18, normalized size = 1.38 \[ \frac{e^{m x} (\cosh (x)-\sinh (x))}{m-1} \]
Antiderivative was successfully verified.
[In] Integrate[E^(m*x)/(Cosh[x] + Sinh[x]),x]
[Out]
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Maple [A] time = 0.004, size = 18, normalized size = 1.4 \[{\frac{{{\rm e}^{mx}}}{ \left ( -1+m \right ) \left ( \cosh \left ( x \right ) +\sinh \left ( x \right ) \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(m*x)/(cosh(x)+sinh(x)),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(m*x)/(cosh(x) + sinh(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203085, size = 34, normalized size = 2.62 \[ \frac{\cosh \left (m x\right ) + \sinh \left (m x\right )}{{\left (m - 1\right )} \cosh \left (x\right ) +{\left (m - 1\right )} \sinh \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(m*x)/(cosh(x) + sinh(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.964104, size = 32, normalized size = 2.46 \[ \begin{cases} \frac{e^{m x}}{m \sinh{\left (x \right )} + m \cosh{\left (x \right )} - \sinh{\left (x \right )} - \cosh{\left (x \right )}} & \text{for}\: m \neq 1 \\\frac{x e^{x}}{\sinh{\left (x \right )} + \cosh{\left (x \right )}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(m*x)/(cosh(x)+sinh(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.203376, size = 22, normalized size = 1.69 \[ \frac{e^{\left (m x\right )}}{m e^{x} - e^{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(m*x)/(cosh(x) + sinh(x)),x, algorithm="giac")
[Out]