Optimal. Leaf size=15 \[ -7+e+x-\frac {3 (-4+x) \log (\log (2))}{x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.20, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {14}
\begin {gather*} \frac {12 \log (\log (2))}{x^2}+x-\frac {3 \log (\log (2))}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {24 \log (\log (2))}{x^3}+\frac {3 \log (\log (2))}{x^2}\right ) \, dx\\ &=x+\frac {12 \log (\log (2))}{x^2}-\frac {3 \log (\log (2))}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.20 \begin {gather*} x+\frac {12 \log (\log (2))}{x^2}-\frac {3 \log (\log (2))}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 19, normalized size = 1.27
method | result | size |
default | \(x +\frac {12 \ln \left (\ln \left (2\right )\right )}{x^{2}}-\frac {3 \ln \left (\ln \left (2\right )\right )}{x}\) | \(19\) |
risch | \(x +\frac {-3 x \ln \left (\ln \left (2\right )\right )+12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\) | \(19\) |
norman | \(\frac {x^{3}-3 x \ln \left (\ln \left (2\right )\right )+12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\) | \(20\) |
gosper | \(-\frac {-x^{3}+3 x \ln \left (\ln \left (2\right )\right )-12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 18, normalized size = 1.20 \begin {gather*} x - \frac {3 \, {\left (x \log \left (\log \left (2\right )\right ) - 4 \, \log \left (\log \left (2\right )\right )\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 16, normalized size = 1.07 \begin {gather*} \frac {x^{3} - 3 \, {\left (x - 4\right )} \log \left (\log \left (2\right )\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 19, normalized size = 1.27 \begin {gather*} x + \frac {- 3 x \log {\left (\log {\left (2 \right )} \right )} + 12 \log {\left (\log {\left (2 \right )} \right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 18, normalized size = 1.20 \begin {gather*} x - \frac {3 \, {\left (x \log \left (\log \left (2\right )\right ) - 4 \, \log \left (\log \left (2\right )\right )\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 18, normalized size = 1.20 \begin {gather*} x+\frac {12\,\ln \left (\ln \left (2\right )\right )-3\,x\,\ln \left (\ln \left (2\right )\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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