Optimal. Leaf size=17 \[ -\frac{1}{4} \cos (2 x)-\frac{1}{8} \cos (4 x) \]
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Rubi [A] time = 0.0075752, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {4284} \[ -\frac{1}{4} \cos (2 x)-\frac{1}{8} \cos (4 x) \]
Antiderivative was successfully verified.
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Rule 4284
Rubi steps
\begin{align*} \int \cos (x) \sin (3 x) \, dx &=-\frac{1}{4} \cos (2 x)-\frac{1}{8} \cos (4 x)\\ \end{align*}
Mathematica [A] time = 0.0051436, size = 17, normalized size = 1. \[ -\frac{1}{2} \cos ^2(x)-\frac{1}{8} \cos (4 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.029, size = 14, normalized size = 0.8 \begin{align*} - \left ( \cos \left ( x \right ) \right ) ^{4}+{\frac{ \left ( \cos \left ( x \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.930472, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{8} \, \cos \left (4 \, x\right ) - \frac{1}{4} \, \cos \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.93429, size = 35, normalized size = 2.06 \begin{align*} -\cos \left (x\right )^{4} + \frac{1}{2} \, \cos \left (x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.512396, size = 22, normalized size = 1.29 \begin{align*} - \frac{\sin{\left (x \right )} \sin{\left (3 x \right )}}{8} - \frac{3 \cos{\left (x \right )} \cos{\left (3 x \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07167, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{8} \, \cos \left (4 \, x\right ) - \frac{1}{4} \, \cos \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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