Optimal. Leaf size=8 \[ 6 \sin \left (\sqrt [6]{x}\right ) \]
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Rubi [A] time = 0.0097518, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {3380, 2637} \[ 6 \sin \left (\sqrt [6]{x}\right ) \]
Antiderivative was successfully verified.
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Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int \frac{\cos \left (\sqrt [6]{x}\right )}{x^{5/6}} \, dx &=6 \operatorname{Subst}\left (\int \cos (x) \, dx,x,\sqrt [6]{x}\right )\\ &=6 \sin \left (\sqrt [6]{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0022308, size = 8, normalized size = 1. \[ 6 \sin \left (\sqrt [6]{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.023, size = 7, normalized size = 0.9 \begin{align*} 6\,\sin \left ( \sqrt [6]{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.74407, size = 8, normalized size = 1. \begin{align*} 6 \, \sin \left (x^{\frac{1}{6}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.8284, size = 22, normalized size = 2.75 \begin{align*} 6 \, \sin \left (x^{\frac{1}{6}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14654, size = 8, normalized size = 1. \begin{align*} 6 \, \sin \left (x^{\frac{1}{6}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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