Optimal. Leaf size=4 \[ \sin (\sin (\sin (x))) \]
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Rubi [A] time = 0.0216749, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {4334, 2637} \[ \sin (\sin (\sin (x))) \]
Antiderivative was successfully verified.
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Rule 4334
Rule 2637
Rubi steps
\begin{align*} \int \cos (x) \cos (\sin (x)) \cos (\sin (\sin (x))) \, dx &=\operatorname{Subst}(\int \cos (x) \cos (\sin (x)) \, dx,x,\sin (x))\\ &=\operatorname{Subst}(\int \cos (x) \, dx,x,\sin (\sin (x)))\\ &=\sin (\sin (\sin (x)))\\ \end{align*}
Mathematica [A] time = 7.6869, size = 4, normalized size = 1. \[ \sin (\sin (\sin (x))) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 5, normalized size = 1.3 \begin{align*} \sin \left ( \sin \left ( \sin \left ( x \right ) \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952398, size = 5, normalized size = 1.25 \begin{align*} \sin \left (\sin \left (\sin \left (x\right )\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.15143, size = 116, normalized size = 29. \begin{align*} \sin \left (\frac{2 \, \tan \left (\frac{\tan \left (\frac{1}{2} \, x\right )}{\tan \left (\frac{1}{2} \, x\right )^{2} + 1}\right )}{\tan \left (\frac{\tan \left (\frac{1}{2} \, x\right )}{\tan \left (\frac{1}{2} \, x\right )^{2} + 1}\right )^{2} + 1}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 12.9891, size = 5, normalized size = 1.25 \begin{align*} \sin{\left (\sin{\left (\sin{\left (x \right )} \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09896, size = 5, normalized size = 1.25 \begin{align*} \sin \left (\sin \left (\sin \left (x\right )\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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