Optimal. Leaf size=4 \[ -\csc (x) \]
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Rubi [A] time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2606, 8} \[ -\csc (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 2606
Rubi steps
\begin {align*} \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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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cot (x) \csc (x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.02, 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 = 0.99, 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 = 0.03, size = 5, normalized size = 1.25
method | result | size |
derivativedivides | \(-\csc \relax (x )\) | \(5\) |
default | \(-\csc \relax (x )\) | \(5\) |
risch | \(-\frac {2 i {\mathrm e}^{i x}}{{\mathrm e}^{2 i x}-1}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, 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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mupad [B] time = 0.21, 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 [A] time = 0.07, size = 5, normalized size = 1.25 \[ - \frac {1}{\sin {\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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