Optimal. Leaf size=11 \[ \frac{\log (\sin (a+b x))}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0040922, 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} \[ \frac{\log (\sin (a+b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3475
Rubi steps
\begin{align*} \int \cot (a+b x) \, dx &=\frac{\log (\sin (a+b x))}{b}\\ \end{align*}
Mathematica [A] time = 0.0106428, size = 19, normalized size = 1.73 \[ \frac{\log (\tan (a+b x))+\log (\cos (a+b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 12, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( \sin \left ( bx+a \right ) \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.970729, size = 15, normalized size = 1.36 \begin{align*} \frac{\log \left (\sin \left (b x + a\right )\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.65546, size = 34, normalized size = 3.09 \begin{align*} \frac{\log \left (\frac{1}{2} \, \sin \left (b x + a\right )\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.411503, size = 17, normalized size = 1.55 \begin{align*} \begin{cases} \frac{\log{\left (\sin{\left (a + b x \right )} \right )}}{b} & \text{for}\: b \neq 0 \\\frac{x \cos{\left (a \right )}}{\sin{\left (a \right )}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18395, size = 16, normalized size = 1.45 \begin{align*} \frac{\log \left ({\left | \sin \left (b x + a\right ) \right |}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]