Optimal. Leaf size=8 \[ \frac{2}{3} \sin (3 x) \]
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Rubi [A] time = 0.0135801, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {4288, 2637} \[ \frac{2}{3} \sin (3 x) \]
Antiderivative was successfully verified.
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Rule 4288
Rule 2637
Rubi steps
\begin{align*} \int \csc (3 x) \sin (6 x) \, dx &=2 \int \cos (3 x) \, dx\\ &=\frac{2}{3} \sin (3 x)\\ \end{align*}
Mathematica [A] time = 0.0030499, size = 8, normalized size = 1. \[ \frac{2}{3} \sin (3 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 9, normalized size = 1.1 \begin{align*}{\frac{2}{3\,\csc \left ( 3\,x \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992151, size = 8, normalized size = 1. \begin{align*} \frac{2}{3} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.47485, size = 19, normalized size = 2.38 \begin{align*} \frac{2}{3} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.92115, size = 7, normalized size = 0.88 \begin{align*} \frac{2 \sin{\left (3 x \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15465, size = 8, normalized size = 1. \begin{align*} \frac{2}{3} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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