Optimal. Leaf size=4 \[ -2 \cos (x) \]
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Rubi [A] time = 0.0118598, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {4287, 2638} \[ -2 \cos (x) \]
Antiderivative was successfully verified.
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Rule 4287
Rule 2638
Rubi steps
\begin{align*} \int \sec (x) \sin (2 x) \, dx &=2 \int \sin (x) \, dx\\ &=-2 \cos (x)\\ \end{align*}
Mathematica [A] time = 0.0014547, size = 4, normalized size = 1. \[ -2 \cos (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 5, normalized size = 1.3 \begin{align*} -2\,\cos \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.927243, size = 5, normalized size = 1.25 \begin{align*} -2 \, \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81245, size = 15, normalized size = 3.75 \begin{align*} -2 \, \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.707154, size = 5, normalized size = 1.25 \begin{align*} - 2 \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09796, size = 5, normalized size = 1.25 \begin{align*} -2 \, \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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