Optimal. Leaf size=8 \[ \frac {\text {Shi}(2 x)}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.375, Rules used = {5448, 12, 3298} \[ \frac {\text {Shi}(2 x)}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 3298
Rule 5448
Rubi steps
\begin {align*} \int \frac {\cosh (x) \sinh (x)}{x} \, dx &=\int \frac {\sinh (2 x)}{2 x} \, dx\\ &=\frac {1}{2} \int \frac {\sinh (2 x)}{x} \, dx\\ &=\frac {\text {Shi}(2 x)}{2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 8, normalized size = 1.00 \[ \frac {\text {Shi}(2 x)}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.85, size = 13, normalized size = 1.62 \[ \frac {1}{4} \, {\rm Ei}\left (2 \, x\right ) - \frac {1}{4} \, {\rm Ei}\left (-2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.13, size = 13, normalized size = 1.62 \[ \frac {1}{4} \, {\rm Ei}\left (2 \, x\right ) - \frac {1}{4} \, {\rm Ei}\left (-2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.13, size = 7, normalized size = 0.88 \[ \frac {\Shi \left (2 x \right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.36, size = 13, normalized size = 1.62 \[ \frac {1}{4} \, {\rm Ei}\left (2 \, x\right ) - \frac {1}{4} \, {\rm Ei}\left (-2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.12 \[ \int \frac {\mathrm {cosh}\relax (x)\,\mathrm {sinh}\relax (x)}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sinh {\relax (x )} \cosh {\relax (x )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________