Optimal. Leaf size=15 \[ \frac{\cosh \left (a+b x^4\right )}{4 b} \]
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Rubi [A] time = 0.0203076, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {5320, 2638} \[ \frac{\cosh \left (a+b x^4\right )}{4 b} \]
Antiderivative was successfully verified.
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Rule 5320
Rule 2638
Rubi steps
\begin{align*} \int x^3 \sinh \left (a+b x^4\right ) \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \sinh (a+b x) \, dx,x,x^4\right )\\ &=\frac{\cosh \left (a+b x^4\right )}{4 b}\\ \end{align*}
Mathematica [A] time = 0.0082737, size = 15, normalized size = 1. \[ \frac{\cosh \left (a+b x^4\right )}{4 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \begin{align*}{\frac{\cosh \left ( b{x}^{4}+a \right ) }{4\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03286, size = 18, normalized size = 1.2 \begin{align*} \frac{\cosh \left (b x^{4} + a\right )}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7345, size = 31, normalized size = 2.07 \begin{align*} \frac{\cosh \left (b x^{4} + a\right )}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.14299, size = 19, normalized size = 1.27 \begin{align*} \begin{cases} \frac{\cosh{\left (a + b x^{4} \right )}}{4 b} & \text{for}\: b \neq 0 \\\frac{x^{4} \sinh{\left (a \right )}}{4} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23275, size = 34, normalized size = 2.27 \begin{align*} \frac{e^{\left (b x^{4} + a\right )} + e^{\left (-b x^{4} - a\right )}}{8 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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