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 {gather*} \begin {aligned} \text {Integral} &=-\text {Subst}(\int 1 \, dx,x,\csc (x))\\ &=-\csc (x)\\ \end {aligned} \end {gather*}
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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 = 0.02, size = 7, normalized size = 1.75
method | result | size |
parallelrisch | \(-\csc \left (x \right )\) | \(5\) |
derivativedivides | \(-\frac {1}{\sin \left (x \right )}\) | \(7\) |
default | \(-\frac {1}{\sin \left (x \right )}\) | \(7\) |
norman | \(\frac {-\frac {1}{2}-\frac {\left (\tan ^{2}\left (\frac {x}{2}\right )\right )}{2}}{\tan \left (\frac {x}{2}\right )}\) | \(18\) |
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 = 0.34, 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 = 0.57, 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 = 0.52, 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 = 0.10, 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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