Optimal. Leaf size=19 \[ \frac{e^{-3 x}}{6}+\frac{e^{5 x}}{10} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0124461, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {2282, 12, 14} \[ \frac{e^{-3 x}}{6}+\frac{e^{5 x}}{10} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2282
Rule 12
Rule 14
Rubi steps
\begin{align*} \int e^x \sinh (4 x) \, dx &=\operatorname{Subst}\left (\int \frac{-1+x^8}{2 x^4} \, dx,x,e^x\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{-1+x^8}{x^4} \, dx,x,e^x\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (-\frac{1}{x^4}+x^4\right ) \, dx,x,e^x\right )\\ &=\frac{e^{-3 x}}{6}+\frac{e^{5 x}}{10}\\ \end{align*}
Mathematica [A] time = 0.0091856, size = 19, normalized size = 1. \[ \frac{e^{-3 x}}{6}+\frac{e^{5 x}}{10} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 26, normalized size = 1.4 \begin{align*} -{\frac{\sinh \left ( 3\,x \right ) }{6}}+{\frac{\sinh \left ( 5\,x \right ) }{10}}+{\frac{\cosh \left ( 3\,x \right ) }{6}}+{\frac{\cosh \left ( 5\,x \right ) }{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09995, size = 18, normalized size = 0.95 \begin{align*} \frac{1}{10} \, e^{\left (5 \, x\right )} + \frac{1}{6} \, e^{\left (-3 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 2.03866, size = 154, normalized size = 8.11 \begin{align*} \frac{4 \,{\left (\cosh \left (x\right )^{4} - \cosh \left (x\right )^{3} \sinh \left (x\right ) + 6 \, \cosh \left (x\right )^{2} \sinh \left (x\right )^{2} - \cosh \left (x\right ) \sinh \left (x\right )^{3} + \sinh \left (x\right )^{4}\right )}}{15 \,{\left (\cosh \left (x\right ) - \sinh \left (x\right )\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.350168, size = 20, normalized size = 1.05 \begin{align*} - \frac{e^{x} \sinh{\left (4 x \right )}}{15} + \frac{4 e^{x} \cosh{\left (4 x \right )}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.09391, size = 18, normalized size = 0.95 \begin{align*} \frac{1}{10} \, e^{\left (5 \, x\right )} + \frac{1}{6} \, e^{\left (-3 \, x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]