Optimal. Leaf size=12 \[ -\frac{\log (\cos (a+b x))}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0044883, antiderivative size = 12, 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} \[ -\frac{\log (\cos (a+b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3475
Rubi steps
\begin{align*} \int \tan (a+b x) \, dx &=-\frac{\log (\cos (a+b x))}{b}\\ \end{align*}
Mathematica [A] time = 0.006467, size = 12, normalized size = 1. \[ -\frac{\log (\cos (a+b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.01, size = 12, normalized size = 1. \begin{align*}{\frac{\ln \left ( \sec \left ( bx+a \right ) \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.988365, size = 24, normalized size = 2. \begin{align*} -\frac{\log \left (-\sin \left (b x + a\right )^{2} + 1\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.92592, size = 31, normalized size = 2.58 \begin{align*} -\frac{\log \left (-\cos \left (b x + a\right )\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sin{\left (a + b x \right )} \sec{\left (a + b x \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20248, size = 24, normalized size = 2. \begin{align*} -\frac{\log \left (\frac{{\left | \cos \left (b x + a\right ) \right |}}{{\left | b \right |}}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]