Optimal. Leaf size=6 \[ \frac{\tan (x)}{2} \]
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Rubi [A] time = 0.0235679, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {8} \[ \frac{\tan (x)}{2} \]
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin{align*} \int \csc (2 x) \tan (x) \, dx &=\operatorname{Subst}\left (\int \frac{1}{2} \, dx,x,\tan (x)\right )\\ &=\frac{\tan (x)}{2}\\ \end{align*}
Mathematica [A] time = 0.0128772, size = 6, normalized size = 1. \[ \frac{\tan (x)}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.014, size = 5, normalized size = 0.8 \begin{align*}{\frac{\tan \left ( x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.932013, size = 36, normalized size = 6. \begin{align*} \frac{\sin \left (2 \, x\right )}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} + 2 \, \cos \left (2 \, x\right ) + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86448, size = 16, normalized size = 2.67 \begin{align*} \frac{1}{2} \, \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.716762, size = 7, normalized size = 1.17 \begin{align*} \frac{\sin{\left (x \right )}}{2 \cos{\left (x \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05491, size = 5, normalized size = 0.83 \begin{align*} \frac{1}{2} \, \tan \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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