Optimal. Leaf size=5 \[ -\sin (\cos (x)) \]
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Rubi [A] time = 0.0088673, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {4335, 2637} \[ -\sin (\cos (x)) \]
Antiderivative was successfully verified.
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Rule 4335
Rule 2637
Rubi steps
\begin{align*} \int \cos (\cos (x)) \sin (x) \, dx &=-\operatorname{Subst}(\int \cos (x) \, dx,x,\cos (x))\\ &=-\sin (\cos (x))\\ \end{align*}
Mathematica [A] time = 2.47877, size = 5, normalized size = 1. \[ -\sin (\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 6, normalized size = 1.2 \begin{align*} -\sin \left ( \cos \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926392, size = 7, normalized size = 1.4 \begin{align*} -\sin \left (\cos \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.28435, size = 59, normalized size = 11.8 \begin{align*} \sin \left (\frac{\tan \left (\frac{1}{2} \, x\right )^{2} - 1}{\tan \left (\frac{1}{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 = 0.505605, size = 5, normalized size = 1. \begin{align*} - \sin{\left (\cos{\left (x \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0521, size = 7, normalized size = 1.4 \begin{align*} -\sin \left (\cos \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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