Optimal. Leaf size=9 \[ \frac {1}{3} \cos (\cos (3 x)) \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {4335, 2638} \[ \frac {1}{3} \cos (\cos (3 x)) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 4335
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*}
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Mathematica [A] time = 2.68, size = 9, normalized size = 1.00 \[ \frac {1}{3} \cos (\cos (3 x)) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.95, size = 22, normalized size = 2.44 \[ \frac {1}{3} \, \cos \left (\frac {\tan \left (\frac {3}{2} \, x\right )^{2} - 1}{\tan \left (\frac {3}{2} \, x\right )^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 7, normalized size = 0.78 \[ \frac {1}{3} \, \cos \left (\cos \left (3 \, x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 8, normalized size = 0.89 \[ \frac {\cos \left (\cos \left (3 x \right )\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 7, normalized size = 0.78 \[ \frac {1}{3} \, \cos \left (\cos \left (3 \, x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.01, size = 7, normalized size = 0.78 \[ \frac {\cos \left (\cos \left (3\,x\right )\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.42, size = 7, normalized size = 0.78 \[ \frac {\cos {\left (\cos {\left (3 x \right )} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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