Optimal. Leaf size=10 \[ \frac {\cosh (a+b x)}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2638} \[ \frac {\cosh (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 2638
Rubi steps
\begin {align*} \int \sinh (a+b x) \, dx &=\frac {\cosh (a+b x)}{b}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 21, normalized size = 2.10 \[ \frac {\sinh (a) \sinh (b x)}{b}+\frac {\cosh (a) \cosh (b x)}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 10, normalized size = 1.00 \[ \frac {\cosh \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.11, size = 26, normalized size = 2.60 \[ \frac {e^{\left (b x + a\right )}}{2 \, b} + \frac {e^{\left (-b x - a\right )}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 11, normalized size = 1.10 \[ \frac {\cosh \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.16, size = 10, normalized size = 1.00 \[ \frac {\cosh \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 10, normalized size = 1.00 \[ \frac {\mathrm {cosh}\left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 12, normalized size = 1.20 \[ \begin {cases} \frac {\cosh {\left (a + b x \right )}}{b} & \text {for}\: b \neq 0 \\x \sinh {\relax (a )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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