Optimal. Leaf size=4 \[ -\csc (x) \]
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Rubi [A] time = 0.02, antiderivative size = 4, normalized size of antiderivative = 1.00, 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} \[ -\csc (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 2606
Rule 4397
Rubi steps
\begin {align*} \int \frac {1}{-\cos (x)+\sec (x)} \, dx &=\int \cot (x) \csc (x) \, dx\\ &=-\operatorname {Subst}(\int 1 \, dx,x,\csc (x))\\ &=-\csc (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 4, normalized size = 1.00 \[ -\csc (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 6, normalized size = 1.50 \[ -\frac {1}{\sin \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 6, normalized size = 1.50 \[ -\frac {1}{\sin \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 7, normalized size = 1.75 \[ -\frac {1}{\sin \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.32, size = 21, normalized size = 5.25 \[ -\frac {\cos \relax (x) + 1}{2 \, \sin \relax (x)} - \frac {\sin \relax (x)}{2 \, {\left (\cos \relax (x) + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.37, size = 6, normalized size = 1.50 \[ -\frac {1}{\sin \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ - \int \frac {1}{\cos {\relax (x )} - \sec {\relax (x )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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