Optimal. Leaf size=2 \[ \text {Ci}(x) \]
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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 = {3383}
\begin {gather*} \text {CosIntegral}(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 3383
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 \begin {gather*} \text {Ci}(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 3, normalized size = 1.50
method | result | size |
default | \(\cosineIntegral \left (x \right )\) | \(3\) |
risch | \(\cosineIntegral \left (x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (x \right )}{2}+\frac {i \pi \,\mathrm {csgn}\left (i x \right )}{2}\) | \(24\) |
meijerg | \(\frac {\sqrt {\pi }\, \left (\frac {2 \gamma +2 \ln \left (x \right )}{\sqrt {\pi }}-\frac {2 \gamma }{\sqrt {\pi }}-\frac {2 \ln \left (2\right )}{\sqrt {\pi }}-\frac {2 \ln \left (\frac {x}{2}\right )}{\sqrt {\pi }}+\frac {2 \cosineIntegral \left (x \right )}{\sqrt {\pi }}\right )}{2}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains complex when optimal does not.
time = 1.53, size = 13, normalized size = 6.50 \begin {gather*} \frac {1}{2} \, {\rm Ei}\left (i \, x\right ) + \frac {1}{2} \, {\rm Ei}\left (-i \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 11 vs.
\(2 (2) = 4\).
time = 0.54, size = 11, normalized size = 5.50 \begin {gather*} \frac {1}{2} \, \operatorname {Ci}\left (-x\right ) + \frac {1}{2} \, \operatorname {Ci}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 12 vs.
\(2 (2) = 4\).
time = 0.49, size = 12, normalized size = 6.00 \begin {gather*} - \log {\left (x \right )} + \frac {\log {\left (x^{2} \right )}}{2} + \operatorname {Ci}{\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.89, size = 2, normalized size = 1.00 \begin {gather*} \operatorname {Ci}\left (x\right ) \end {gather*}
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 \begin {gather*} \mathrm {cosint}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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