Optimal. Leaf size=2 \[ \text{CosIntegral}(x) \]
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Rubi [A] time = 0.0124961, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {3302} \[ \text{CosIntegral}(x) \]
Antiderivative was successfully verified.
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Rule 3302
Rubi steps
\begin{align*} \int \frac{\cos (x)}{x} \, dx &=\text{Ci}(x)\\ \end{align*}
Mathematica [A] time = 0.0014025, size = 2, normalized size = 1. \[ \text{CosIntegral}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 3, normalized size = 1.5 \begin{align*}{\it Ci} \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 1.05578, size = 18, normalized size = 9. \begin{align*} \frac{1}{2} \,{\rm Ei}\left (i \, x\right ) + \frac{1}{2} \,{\rm Ei}\left (-i \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.69277, size = 59, normalized size = 29.5 \begin{align*} \frac{1}{2} \, \operatorname{Ci}\left (-x\right ) + \frac{1}{2} \, \operatorname{Ci}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.16375, size = 12, normalized size = 6. \begin{align*} - \log{\left (x \right )} + \frac{\log{\left (x^{2} \right )}}{2} + \operatorname{Ci}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09193, size = 3, normalized size = 1.5 \begin{align*} \operatorname{Ci}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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