Optimal. Leaf size=10 \[ \frac{\sec (a+b x)}{b} \]
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Rubi [A] time = 0.0107023, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {2606, 8} \[ \frac{\sec (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 2606
Rule 8
Rubi steps
\begin{align*} \int \sec (a+b x) \tan (a+b x) \, dx &=\frac{\operatorname{Subst}(\int 1 \, dx,x,\sec (a+b x))}{b}\\ &=\frac{\sec (a+b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.006631, size = 10, normalized size = 1. \[ \frac{\sec (a+b x)}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 11, normalized size = 1.1 \begin{align*}{\frac{\sec \left ( bx+a \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974452, size = 16, normalized size = 1.6 \begin{align*} \frac{1}{b \cos \left (b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87666, size = 27, normalized size = 2.7 \begin{align*} \frac{1}{b \cos \left (b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sin{\left (a + b x \right )} \sec ^{2}{\left (a + b x \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1312, size = 16, normalized size = 1.6 \begin{align*} \frac{1}{b \cos \left (b x + a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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