Optimal. Leaf size=2 \[ \operatorname {CosIntegral}(x) \]
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Rubi [A] time = 0.01, antiderivative size = 2, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 2, normalized size = 1.00 \[ \operatorname {CosIntegral}(x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 11, normalized size = 5.50 \[ \frac {1}{2} \, \operatorname {Ci}\left (-x\right ) + \frac {1}{2} \, \operatorname {Ci}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.30, size = 2, normalized size = 1.00 \[ \operatorname {Ci}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 3, normalized size = 1.50 \[ \Ci \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.57, size = 13, normalized size = 6.50 \[ \frac {1}{2} \, {\rm Ei}\left (i \, x\right ) + \frac {1}{2} \, {\rm Ei}\left (-i \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.50 \[ \mathrm {cosint}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.00, size = 12, normalized size = 6.00 \[ - \log {\relax (x )} + \frac {\log {\left (x^{2} \right )}}{2} + \operatorname {Ci}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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