Optimal. Leaf size=8 \[ \frac {\sin ^2(x)}{2} \]
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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 = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2564, 30} \[ \frac {\sin ^2(x)}{2} \]
Antiderivative was successfully verified.
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Rule 30
Rule 2564
Rubi steps
\begin {align*} \int \cos (x) \sin (x) \, dx &=\operatorname {Subst}(\int x \, dx,x,\sin (x))\\ &=\frac {\sin ^2(x)}{2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ -\frac {1}{2} \cos ^2(x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 6, normalized size = 0.75 \[ -\frac {1}{2} \, \cos \relax (x)^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 6, normalized size = 0.75 \[ -\frac {1}{2} \, \cos \relax (x)^{2} \]
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 \[ \frac {\left (\sin ^{2}\relax (x )\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 6, normalized size = 0.75 \[ -\frac {1}{2} \, \cos \relax (x)^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 6, normalized size = 0.75 \[ \frac {{\sin \relax (x)}^2}{2} \]
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 \[ \frac {\sin ^{2}{\relax (x )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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