Optimal. Leaf size=14 \[ \frac {x}{2}+\frac {1}{2} \sin (x) \cos (x) \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2635, 8} \[ \frac {x}{2}+\frac {1}{2} \sin (x) \cos (x) \]
Antiderivative was successfully verified.
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Rule 8
Rule 2635
Rubi steps
\begin {align*} \int \cos ^2(x) \, dx &=\frac {1}{2} \cos (x) \sin (x)+\frac {\int 1 \, dx}{2}\\ &=\frac {x}{2}+\frac {1}{2} \cos (x) \sin (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {x}{2}+\frac {1}{4} \sin (2 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 10, normalized size = 0.71 \[ \frac {1}{2} \, \cos \relax (x) \sin \relax (x) + \frac {1}{2} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 10, normalized size = 0.71 \[ \frac {1}{2} \, x + \frac {1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.79 \[ \frac {\cos \relax (x ) \sin \relax (x )}{2}+\frac {x}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 10, normalized size = 0.71 \[ \frac {1}{2} \, x + \frac {1}{4} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 10, normalized size = 0.71 \[ \frac {x}{2}+\frac {\sin \left (2\,x\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 0.71 \[ \frac {x}{2} + \frac {\sin {\relax (x )} \cos {\relax (x )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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