Optimal. Leaf size=2 \[ \sec (x) \]
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Rubi [A] time = 0.0187821, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {4397, 2606, 8} \[ \sec (x) \]
Antiderivative was successfully verified.
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Rule 4397
Rule 2606
Rule 8
Rubi steps
\begin{align*} \int \frac{1}{\csc (x)-\sin (x)} \, dx &=\int \sec (x) \tan (x) \, dx\\ &=\operatorname{Subst}(\int 1 \, dx,x,\sec (x))\\ &=\sec (x)\\ \end{align*}
Mathematica [A] time = 0.0038522, size = 2, normalized size = 1. \[ \sec (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.03, size = 5, normalized size = 2.5 \begin{align*} \left ( \cos \left ( x \right ) \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.963639, size = 23, normalized size = 11.5 \begin{align*} -\frac{2}{\frac{\sin \left (x\right )^{2}}{{\left (\cos \left (x\right ) + 1\right )}^{2}} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.97604, size = 14, normalized size = 7. \begin{align*} \frac{1}{\cos \left (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}{- \sin{\left (x \right )} + \csc{\left (x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.15938, size = 23, normalized size = 11.5 \begin{align*} \frac{2}{\frac{\cos \left (x\right ) - 1}{\cos \left (x\right ) + 1} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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