Optimal. Leaf size=4 \[ \sin (\sin (\sin (x))) \]
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Rubi [A] time = 0.02, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {4334, 2637} \[ \sin (\sin (\sin (x))) \]
Antiderivative was successfully verified.
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Rule 2637
Rule 4334
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*}
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Mathematica [A] time = 8.96, size = 4, normalized size = 1.00 \[ \sin (\sin (\sin (x))) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.67, size = 41, normalized size = 10.25 \[ \sin \left (\frac {2 \, \tan \left (\frac {\tan \left (\frac {1}{2} \, x\right )}{\tan \left (\frac {1}{2} \, x\right )^{2} + 1}\right )}{\tan \left (\frac {\tan \left (\frac {1}{2} \, x\right )}{\tan \left (\frac {1}{2} \, x\right )^{2} + 1}\right )^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 4, normalized size = 1.00 \[ \sin \left (\sin \left (\sin \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 5, normalized size = 1.25 \[ \sin \left (\sin \left (\sin \relax (x )\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 4, normalized size = 1.00 \[ \sin \left (\sin \left (\sin \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.00, size = 4, normalized size = 1.00 \[ \sin \left (\sin \left (\sin \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 8.85, size = 5, normalized size = 1.25 \[ \sin {\left (\sin {\left (\sin {\relax (x )} \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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