Optimal. Leaf size=7 \[ \frac {\sin (x)}{\log (x)} \]
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Rubi [F]
time = 0.10, 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 {\cos (x) \log (x)-\frac {\sin (x)}{x}}{\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left (\frac {\cos (x)}{\log (x)}-\frac {\sin (x)}{x \log ^2(x)}\right ) \, dx\\ &=\int \frac {\cos (x)}{\log (x)} \, dx-\int \frac {\sin (x)}{x \log ^2(x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.45, size = 7, normalized size = 1.00 \begin {gather*} \frac {\sin (x)}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 8, normalized size = 1.14
method | result | size |
risch | \(\frac {\sin \left (x \right )}{\ln \left (x \right )}\) | \(8\) |
parallelrisch | \(\frac {\sin \left (x \right )}{\ln \left (x \right )}\) | \(8\) |
norman | \(\frac {2 \tan \left (\frac {x}{2}\right )}{\left (1+\tan ^{2}\left (\frac {x}{2}\right )\right ) \ln \left (x \right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.43, size = 7, normalized size = 1.00 \begin {gather*} \frac {\sin \left (x\right )}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 7, normalized size = 1.00 \begin {gather*} \frac {\sin \left (x\right )}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.51, size = 5, normalized size = 0.71 \begin {gather*} \frac {\sin {\left (x \right )}}{\log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 20 vs.
\(2 (7) = 14\).
time = 0.89, size = 20, normalized size = 2.86 \begin {gather*} \frac {2 \, \tan \left (\frac {1}{2} \, x\right )}{\log \left (x\right ) \tan \left (\frac {1}{2} \, x\right )^{2} + \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.28, size = 7, normalized size = 1.00 \begin {gather*} \frac {\sin \left (x\right )}{\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 19, normalized size = 2.71 \begin {gather*} -\frac {\cos \left (x \right )}{\ln \left (x \right )}+\frac {\sin \left (x \right )}{x \ln \left (x \right )} \end {gather*}
Warning: Unable to verify antiderivative.
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