Optimal. Leaf size=8 \[ \frac{\text{Si}(2 x)}{2} \]
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Rubi [A] time = 0.0285319, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {4406, 12, 3299} \[ \frac{\text{Si}(2 x)}{2} \]
Antiderivative was successfully verified.
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Rule 4406
Rule 12
Rule 3299
Rubi steps
\begin{align*} \int \frac{\cos (x) \sin (x)}{x} \, dx &=\int \frac{\sin (2 x)}{2 x} \, dx\\ &=\frac{1}{2} \int \frac{\sin (2 x)}{x} \, dx\\ &=\frac{\text{Si}(2 x)}{2}\\ \end{align*}
Mathematica [A] time = 0.0058604, size = 8, normalized size = 1. \[ \frac{\text{Si}(2 x)}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.026, size = 7, normalized size = 0.9 \begin{align*}{\frac{{\it Si} \left ( 2\,x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 1.21864, size = 18, normalized size = 2.25 \begin{align*} -\frac{1}{4} i \,{\rm Ei}\left (2 i \, x\right ) + \frac{1}{4} i \,{\rm Ei}\left (-2 i \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.451929, size = 31, normalized size = 3.88 \begin{align*} \frac{1}{2} \, \operatorname{Si}\left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.07542, size = 5, normalized size = 0.62 \begin{align*} \frac{\operatorname{Si}{\left (2 x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11652, size = 8, normalized size = 1. \begin{align*} \frac{1}{2} \, \operatorname{Si}\left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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