Optimal. Leaf size=16 \[ \frac{2 F\left (\left .\frac{1}{2} (a+b x)\right |2\right )}{b} \]
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Rubi [A] time = 0.0091666, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {2641} \[ \frac{2 F\left (\left .\frac{1}{2} (a+b x)\right |2\right )}{b} \]
Antiderivative was successfully verified.
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Rule 2641
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{\cos (a+b x)}} \, dx &=\frac{2 F\left (\left .\frac{1}{2} (a+b x)\right |2\right )}{b}\\ \end{align*}
Mathematica [A] time = 0.0154516, size = 16, normalized size = 1. \[ \frac{2 F\left (\left .\frac{1}{2} (a+b x)\right |2\right )}{b} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.03, size = 18, normalized size = 1.1 \begin{align*} 2\,{\frac{{\it InverseJacobiAM} \left ( 1/2\,bx+a/2,\sqrt{2} \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{\cos \left (b x + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{\sqrt{\cos \left (b x + a\right )}}, x\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 \frac{1}{\sqrt{\cos{\left (a + b x \right )}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{\cos \left (b x + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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