Optimal. Leaf size=17 \[ \frac {1}{4} \cos (2 x)-\frac {1}{16} \cos (8 x) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {4284} \[ \frac {1}{4} \cos (2 x)-\frac {1}{16} \cos (8 x) \]
Antiderivative was successfully verified.
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Rule 4284
Rubi steps
\begin {align*} \int \cos (5 x) \sin (3 x) \, dx &=\frac {1}{4} \cos (2 x)-\frac {1}{16} \cos (8 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \frac {\cos ^2(x)}{2}-\frac {1}{16} \cos (8 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 25, normalized size = 1.47 \[ -8 \, \cos \relax (x)^{8} + 16 \, \cos \relax (x)^{6} - 10 \, \cos \relax (x)^{4} + \frac {5}{2} \, \cos \relax (x)^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.80, size = 13, normalized size = 0.76 \[ -\frac {1}{16} \, \cos \left (8 \, x\right ) + \frac {1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 14, normalized size = 0.82 \[ \frac {\cos \left (2 x \right )}{4}-\frac {\cos \left (8 x \right )}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 13, normalized size = 0.76 \[ -\frac {1}{16} \, \cos \left (8 \, x\right ) + \frac {1}{4} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 13, normalized size = 0.76 \[ \frac {\cos \left (2\,x\right )}{4}-\frac {\cos \left (8\,x\right )}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.52, size = 26, normalized size = 1.53 \[ \frac {5 \sin {\left (3 x \right )} \sin {\left (5 x \right )}}{16} + \frac {3 \cos {\left (3 x \right )} \cos {\left (5 x \right )}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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