Optimal. Leaf size=2 \[ \sec (x) \]
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Rubi [A] time = 0.02, antiderivative size = 2, 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} \[ \sec (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 2606
Rule 4397
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*}
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Mathematica [A] time = 0.00, size = 2, normalized size = 1.00 \[ \sec (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 2.20, size = 4, normalized size = 2.00 \[ \frac {1}{\cos \relax (x)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.14, size = 17, normalized size = 8.50 \[ \frac {2}{\frac {\cos \relax (x) - 1}{\cos \relax (x) + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 5, normalized size = 2.50 \[ \frac {1}{\cos \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.31, size = 17, normalized size = 8.50 \[ -\frac {2}{\frac {\sin \relax (x)^{2}}{{\left (\cos \relax (x) + 1\right )}^{2}} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.46, size = 12, normalized size = 6.00 \[ -\frac {2}{{\mathrm {tan}\left (\frac {x}{2}\right )}^2-1} \]
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 \[ \int \frac {1}{- \sin {\relax (x )} + \csc {\relax (x )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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