Optimal. Leaf size=8 \[ -2 \csc \left (\sqrt{x}\right ) \]
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Rubi [A] time = 0.196644, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {6715, 2606, 8} \[ -2 \csc \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Rule 6715
Rule 2606
Rule 8
Rubi steps
\begin{align*} \int \frac{\cot \left (\sqrt{x}\right ) \csc \left (\sqrt{x}\right )}{\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int \cot (x) \csc (x) \, dx,x,\sqrt{x}\right )\\ &=-\left (2 \operatorname{Subst}\left (\int 1 \, dx,x,\csc \left (\sqrt{x}\right )\right )\right )\\ &=-2 \csc \left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0179433, size = 8, normalized size = 1. \[ -2 \csc \left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.016, size = 7, normalized size = 0.9 \begin{align*} -2\,\csc \left ( \sqrt{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952835, size = 11, normalized size = 1.38 \begin{align*} -\frac{2}{\sin \left (\sqrt{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.0916, size = 23, normalized size = 2.88 \begin{align*} -\frac{2}{\sin \left (\sqrt{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.327789, size = 8, normalized size = 1. \begin{align*} - 2 \csc{\left (\sqrt{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06237, size = 11, normalized size = 1.38 \begin{align*} -\frac{2}{\sin \left (\sqrt{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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