Optimal. Leaf size=12 \[ a x+b \sinh (x)+c \cosh (x) \]
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Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2637, 2638} \[ a x+b \sinh (x)+c \cosh (x) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 2638
Rubi steps
\begin {align*} \int (a+b \cosh (x)+c \sinh (x)) \, dx &=a x+b \int \cosh (x) \, dx+c \int \sinh (x) \, dx\\ &=a x+c \cosh (x)+b \sinh (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ a x+b \sinh (x)+c \cosh (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 12, normalized size = 1.00 \[ a x + c \cosh \relax (x) + b \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.11, size = 26, normalized size = 2.17 \[ a x + \frac {1}{2} \, c {\left (e^{\left (-x\right )} + e^{x}\right )} - \frac {1}{2} \, b {\left (e^{\left (-x\right )} - e^{x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 1.08 \[ a x +c \cosh \relax (x )+b \sinh \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 12, normalized size = 1.00 \[ a x + c \cosh \relax (x) + b \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 12, normalized size = 1.00 \[ a\,x+c\,\mathrm {cosh}\relax (x)+b\,\mathrm {sinh}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 1.00 \[ a x + b \sinh {\relax (x )} + c \cosh {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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