Optimal. Leaf size=4 \[ -\csc (x) \]
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Rubi [A]
time = 0.00, 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 = {2686, 8}
\begin {gather*} -\csc (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 2686
Rubi steps
\begin {align*} \int \cot (x) \csc (x) \, dx &=-\text {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 \begin {gather*} -\csc (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 5, normalized size = 1.25
method | result | size |
derivativedivides | \(-\csc \left (x \right )\) | \(5\) |
default | \(-\csc \left (x \right )\) | \(5\) |
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 = 2.31, size = 6, normalized size = 1.50 \begin {gather*} -\frac {1}{\sin \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.88, size = 6, normalized size = 1.50 \begin {gather*} -\frac {1}{\sin \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 5, normalized size = 1.25 \begin {gather*} - \frac {1}{\sin {\left (x \right )}} \end {gather*}
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 \begin {gather*} -\frac {1}{\sin \left (x\right )} \end {gather*}
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 \begin {gather*} -\frac {1}{\sin \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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