Optimal. Leaf size=15 \[ \frac {\log (x)}{2}-\frac {1}{2} \operatorname {CosIntegral}(2 x) \]
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Rubi [A] time = 0.04, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3312, 3302} \[ \frac {\log (x)}{2}-\frac {1}{2} \text {CosIntegral}(2 x) \]
Antiderivative was successfully verified.
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Rule 3302
Rule 3312
Rubi steps
\begin {align*} \int \frac {\sin ^2(x)}{x} \, dx &=\int \left (\frac {1}{2 x}-\frac {\cos (2 x)}{2 x}\right ) \, dx\\ &=\frac {\log (x)}{2}-\frac {1}{2} \int \frac {\cos (2 x)}{x} \, dx\\ &=-\frac {\text {Ci}(2 x)}{2}+\frac {\log (x)}{2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \[ \frac {\log (x)}{2}-\frac {1}{2} \operatorname {CosIntegral}(2 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 17, normalized size = 1.13 \[ -\frac {1}{4} \, \operatorname {Ci}\left (2 \, x\right ) - \frac {1}{4} \, \operatorname {Ci}\left (-2 \, x\right ) + \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 11, normalized size = 0.73 \[ -\frac {1}{2} \, \operatorname {Ci}\left (2 \, x\right ) + \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 0.80 \[ -\frac {\Ci \left (2 x \right )}{2}+\frac {\ln \relax (x )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.56, size = 17, normalized size = 1.13 \[ -\frac {1}{4} \, {\rm Ei}\left (2 i \, x\right ) - \frac {1}{4} \, {\rm Ei}\left (-2 i \, x\right ) + \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \frac {\ln \relax (x)}{2}-\frac {\mathrm {cosint}\left (2\,x\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.08, size = 10, normalized size = 0.67 \[ \frac {\log {\relax (x )}}{2} - \frac {\operatorname {Ci}{\left (2 x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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