Optimal. Leaf size=8 \[ -\frac{1}{6} \cos ^6(x) \]
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Rubi [A] time = 0.0125415, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {2565, 30} \[ -\frac{1}{6} \cos ^6(x) \]
Antiderivative was successfully verified.
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Rule 2565
Rule 30
Rubi steps
\begin{align*} \int \cos ^5(x) \sin (x) \, dx &=-\operatorname{Subst}\left (\int x^5 \, dx,x,\cos (x)\right )\\ &=-\frac{1}{6} \cos ^6(x)\\ \end{align*}
Mathematica [A] time = 0.0012081, size = 8, normalized size = 1. \[ -\frac{1}{6} \cos ^6(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 7, normalized size = 0.9 \begin{align*} -{\frac{ \left ( \cos \left ( x \right ) \right ) ^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.927721, size = 8, normalized size = 1. \begin{align*} -\frac{1}{6} \, \cos \left (x\right )^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.95143, size = 20, normalized size = 2.5 \begin{align*} -\frac{1}{6} \, \cos \left (x\right )^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.055917, size = 7, normalized size = 0.88 \begin{align*} - \frac{\cos ^{6}{\left (x \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05263, size = 8, normalized size = 1. \begin{align*} -\frac{1}{6} \, \cos \left (x\right )^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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