Optimal. Leaf size=26 \[ \text {Ei}(-\log (x))-\frac {\log (\log (x) \sin (x))}{x}+\text {Int}\left (\frac {\cot (x)}{x},x\right ) \]
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Rubi [A]
time = 0.25, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\log (\log (x) \sin (x))}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log (\log (x) \sin (x))}{x^2} \, dx &=-\frac {\log (\log (x) \sin (x))}{x}-\int \frac {-1-x \cot (x) \log (x)}{x^2 \log (x)} \, dx\\ &=-\frac {\log (\log (x) \sin (x))}{x}-\int \left (-\frac {\cot (x)}{x}-\frac {1}{x^2 \log (x)}\right ) \, dx\\ &=-\frac {\log (\log (x) \sin (x))}{x}+\int \frac {\cot (x)}{x} \, dx+\int \frac {1}{x^2 \log (x)} \, dx\\ &=-\frac {\log (\log (x) \sin (x))}{x}+\int \frac {\cot (x)}{x} \, dx+\text {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (x)\right )\\ &=\text {Ei}(-\log (x))-\frac {\log (\log (x) \sin (x))}{x}+\int \frac {\cot (x)}{x} \, dx\\ \end {align*}
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Mathematica [A]
time = 1.40, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log (\log (x) \sin (x))}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (\ln \left (x \right ) \sin \left (x \right )\right )}{x^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log {\left (\log {\left (x \right )} \sin {\left (x \right )} \right )}}{x^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (\ln \left (x\right )\,\sin \left (x\right )\right )}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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