Optimal. Leaf size=15 \[ -\frac{\cosh \left (a+\frac{b}{x^2}\right )}{2 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0194359, 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} \[ -\frac{\cosh \left (a+\frac{b}{x^2}\right )}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 5320
Rule 2638
Rubi steps
\begin{align*} \int \frac{\sinh \left (a+\frac{b}{x^2}\right )}{x^3} \, dx &=-\left (\frac{1}{2} \operatorname{Subst}\left (\int \sinh (a+b x) \, dx,x,\frac{1}{x^2}\right )\right )\\ &=-\frac{\cosh \left (a+\frac{b}{x^2}\right )}{2 b}\\ \end{align*}
Mathematica [A] time = 0.0046271, size = 15, normalized size = 1. \[ -\frac{\cosh \left (a+\frac{b}{x^2}\right )}{2 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 14, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,b}\cosh \left ( a+{\frac{b}{{x}^{2}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.1396, size = 18, normalized size = 1.2 \begin{align*} -\frac{\cosh \left (a + \frac{b}{x^{2}}\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.61495, size = 41, normalized size = 2.73 \begin{align*} -\frac{\cosh \left (\frac{a x^{2} + b}{x^{2}}\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 4.68851, size = 22, normalized size = 1.47 \begin{align*} \begin{cases} - \frac{\cosh{\left (a + \frac{b}{x^{2}} \right )}}{2 b} & \text{for}\: b \neq 0 \\- \frac{\sinh{\left (a \right )}}{2 x^{2}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.2381, size = 34, normalized size = 2.27 \begin{align*} -\frac{e^{\left (a + \frac{b}{x^{2}}\right )} + e^{\left (-a - \frac{b}{x^{2}}\right )}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]