Optimal. Leaf size=17 \[ \frac {1}{10} \sinh (5 x)-\frac {1}{6} \sinh (3 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {4282} \[ \frac {1}{10} \sinh (5 x)-\frac {1}{6} \sinh (3 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4282
Rubi steps
\begin {align*} \int \sinh (x) \sinh (4 x) \, dx &=-\frac {1}{6} \sinh (3 x)+\frac {1}{10} \sinh (5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \frac {1}{10} \sinh (5 x)-\frac {1}{6} \sinh (3 x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.41, size = 36, normalized size = 2.12 \[ \frac {1}{10} \, \sinh \relax (x)^{5} + \frac {1}{6} \, {\left (6 \, \cosh \relax (x)^{2} - 1\right )} \sinh \relax (x)^{3} + \frac {1}{2} \, {\left (\cosh \relax (x)^{4} - \cosh \relax (x)^{2}\right )} \sinh \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.13, size = 27, normalized size = 1.59 \[ \frac {1}{60} \, {\left (5 \, e^{\left (2 \, x\right )} - 3\right )} e^{\left (-5 \, x\right )} + \frac {1}{20} \, e^{\left (5 \, x\right )} - \frac {1}{12} \, e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.16, size = 14, normalized size = 0.82 \[ -\frac {\sinh \left (3 x \right )}{6}+\frac {\sinh \left (5 x \right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.48, size = 27, normalized size = 1.59 \[ -\frac {1}{60} \, {\left (5 \, e^{\left (-2 \, x\right )} - 3\right )} e^{\left (5 \, x\right )} + \frac {1}{12} \, e^{\left (-3 \, x\right )} - \frac {1}{20} \, e^{\left (-5 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 14, normalized size = 0.82 \[ \frac {4\,{\mathrm {sinh}\relax (x)}^3\,\left (6\,{\mathrm {sinh}\relax (x)}^2+5\right )}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.41, size = 20, normalized size = 1.18 \[ \frac {4 \sinh {\relax (x )} \cosh {\left (4 x \right )}}{15} - \frac {\sinh {\left (4 x \right )} \cosh {\relax (x )}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________