Optimal. Leaf size=7 \[ \log (\sinh (x)+i) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0184888, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {2667, 31} \[ \log (\sinh (x)+i) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2667
Rule 31
Rubi steps
\begin{align*} \int \frac{\cosh (x)}{i+\sinh (x)} \, dx &=\operatorname{Subst}\left (\int \frac{1}{i+x} \, dx,x,\sinh (x)\right )\\ &=\log (i+\sinh (x))\\ \end{align*}
Mathematica [A] time = 0.0053324, size = 7, normalized size = 1. \[ \log (\sinh (x)+i) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.008, size = 7, normalized size = 1. \begin{align*} \ln \left ( i+\sinh \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.18454, size = 7, normalized size = 1. \begin{align*} \log \left (\sinh \left (x\right ) + i\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.82319, size = 28, normalized size = 4. \begin{align*} -x + 2 \, \log \left (e^{x} + i\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.147357, size = 8, normalized size = 1.14 \begin{align*} - x + 2 \log{\left (e^{x} + i \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.3252, size = 15, normalized size = 2.14 \begin{align*} -x + 2 \, \log \left (e^{x} + i\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]