Optimal. Leaf size=11 \[ \frac{\log (\cosh (a+b x))}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0057195, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {3475} \[ \frac{\log (\cosh (a+b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3475
Rubi steps
\begin{align*} \int \tanh (a+b x) \, dx &=\frac{\log (\cosh (a+b x))}{b}\\ \end{align*}
Mathematica [A] time = 0.0052227, size = 11, normalized size = 1. \[ \frac{\log (\cosh (a+b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.003, size = 30, normalized size = 2.7 \begin{align*} -{\frac{\ln \left ( -1+\tanh \left ( bx+a \right ) \right ) }{2\,b}}-{\frac{\ln \left ( 1+\tanh \left ( bx+a \right ) \right ) }{2\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.0177, size = 15, normalized size = 1.36 \begin{align*} \frac{\log \left (\cosh \left (b x + a\right )\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 2.19036, size = 88, normalized size = 8. \begin{align*} -\frac{b x - \log \left (\frac{2 \, \cosh \left (b x + a\right )}{\cosh \left (b x + a\right ) - \sinh \left (b x + a\right )}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.151378, size = 17, normalized size = 1.55 \begin{align*} \begin{cases} x - \frac{\log{\left (\tanh{\left (a + b x \right )} + 1 \right )}}{b} & \text{for}\: b \neq 0 \\x \tanh{\left (a \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.22161, size = 36, normalized size = 3.27 \begin{align*} -\frac{b x + a}{b} + \frac{\log \left (e^{\left (2 \, b x + 2 \, a\right )} + 1\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]