Optimal. Leaf size=8 \[ \frac {\sin ^3(x)}{3} \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, 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 = {2564, 30} \[ \frac {\sin ^3(x)}{3} \]
Antiderivative was successfully verified.
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Rule 30
Rule 2564
Rubi steps
\begin {align*} \int \cos (x) \sin ^2(x) \, dx &=\operatorname {Subst}\left (\int x^2 \, dx,x,\sin (x)\right )\\ &=\frac {\sin ^3(x)}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {\sin ^3(x)}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 10, normalized size = 1.25 \[ -\frac {1}{3} \, {\left (\cos \relax (x)^{2} - 1\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, \sin \relax (x)^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 0.88 \[ \frac {\left (\sin ^{3}\relax (x )\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, \sin \relax (x)^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 6, normalized size = 0.75 \[ \frac {{\sin \relax (x)}^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 5, normalized size = 0.62 \[ \frac {\sin ^{3}{\relax (x )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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