Optimal. Leaf size=9 \[ \frac{1}{3} \cos (\cos (3 x)) \]
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Rubi [A] time = 0.0107249, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {4335, 2638} \[ \frac{1}{3} \cos (\cos (3 x)) \]
Antiderivative was successfully verified.
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Rule 4335
Rule 2638
Rubi steps
\begin{align*} \int \sin (3 x) \sin (\cos (3 x)) \, dx &=-\left (\frac{1}{3} \operatorname{Subst}(\int \sin (x) \, dx,x,\cos (3 x))\right )\\ &=\frac{1}{3} \cos (\cos (3 x))\\ \end{align*}
Mathematica [A] time = 2.75389, size = 9, normalized size = 1. \[ \frac{1}{3} \cos (\cos (3 x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 8, normalized size = 0.9 \begin{align*}{\frac{\cos \left ( \cos \left ( 3\,x \right ) \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960353, size = 9, normalized size = 1. \begin{align*} \frac{1}{3} \, \cos \left (\cos \left (3 \, x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.99499, size = 65, normalized size = 7.22 \begin{align*} \frac{1}{3} \, \cos \left (\frac{\tan \left (\frac{3}{2} \, x\right )^{2} - 1}{\tan \left (\frac{3}{2} \, x\right )^{2} + 1}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.532767, size = 7, normalized size = 0.78 \begin{align*} \frac{\cos{\left (\cos{\left (3 x \right )} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10921, size = 9, normalized size = 1. \begin{align*} \frac{1}{3} \, \cos \left (\cos \left (3 \, x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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