Optimal. Leaf size=14 \[ \text {Int}(x \cot (x) \csc (x) \cos (k \csc (x)),x) \]
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Rubi [A] time = 0.44, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx &=\int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx\\ \end {align*}
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Mathematica [A] time = 0.13, size = 0, normalized size = 0.00 \[ \int x \cos (k \csc (x)) \cot (x) \csc (x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {x \cos \relax (x) \cos \left (\frac {k}{\sin \relax (x)}\right )}{\cos \relax (x)^{2} - 1}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x \cos \relax (x) \cos \left (\frac {k}{\sin \relax (x)}\right )}{\sin \relax (x)^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.21, size = 0, normalized size = 0.00 \[ \int \frac {x \cos \relax (x ) \cos \left (\frac {k}{\sin \relax (x )}\right )}{\sin \relax (x )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 240, normalized size = 17.14 \[ -\frac {{\left (x e^{\left (\frac {4 \, k \cos \left (2 \, x\right ) \cos \relax (x)}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1} + \frac {4 \, k \sin \left (2 \, x\right ) \sin \relax (x)}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1}\right )} + x e^{\left (\frac {4 \, k \cos \relax (x)}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1}\right )}\right )} e^{\left (-\frac {2 \, k \cos \left (2 \, x\right ) \cos \relax (x)}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1} - \frac {2 \, k \sin \left (2 \, x\right ) \sin \relax (x)}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1} - \frac {2 \, k \cos \relax (x)}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1}\right )} \sin \left (\frac {2 \, {\left (k \cos \relax (x) \sin \left (2 \, x\right ) - k \cos \left (2 \, x\right ) \sin \relax (x) + k \sin \relax (x)\right )}}{\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \cos \left (2 \, x\right ) + 1}\right )}{2 \, k} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {x\,\cos \left (\frac {k}{\sin \relax (x)}\right )\,\cos \relax (x)}{{\sin \relax (x)}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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