Optimal. Leaf size=25 \[ 2+2 x+\log (x)-\frac {6}{\log \left (\log (x)-(x+7 \log (x))^2\right )} \]
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Rubi [A]
time = 0.32, antiderivative size = 30, normalized size of antiderivative = 1.20, number of steps
used = 5, number of rules used = 3, integrand size = 123, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6874, 45,
6818} \begin {gather*} -\frac {6}{\log \left (-x^2-49 \log ^2(x)-14 x \log (x)+\log (x)\right )}+2 x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 6818
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1+2 x}{x}+\frac {6 \left (-1+14 x+2 x^2+98 \log (x)+14 x \log (x)\right )}{x \left (x^2-\log (x)+14 x \log (x)+49 \log ^2(x)\right ) \log ^2\left (-x^2+\log (x)-14 x \log (x)-49 \log ^2(x)\right )}\right ) \, dx\\ &=6 \int \frac {-1+14 x+2 x^2+98 \log (x)+14 x \log (x)}{x \left (x^2-\log (x)+14 x \log (x)+49 \log ^2(x)\right ) \log ^2\left (-x^2+\log (x)-14 x \log (x)-49 \log ^2(x)\right )} \, dx+\int \frac {1+2 x}{x} \, dx\\ &=-\frac {6}{\log \left (-x^2+\log (x)-14 x \log (x)-49 \log ^2(x)\right )}+\int \left (2+\frac {1}{x}\right ) \, dx\\ &=2 x+\log (x)-\frac {6}{\log \left (-x^2+\log (x)-14 x \log (x)-49 \log ^2(x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 30, normalized size = 1.20 \begin {gather*} 2 x+\log (x)-\frac {6}{\log \left (-x^2+\log (x)-14 x \log (x)-49 \log ^2(x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.06, size = 31, normalized size = 1.24
method | result | size |
default | \(2 x +\ln \left (x \right )-\frac {6}{\ln \left (-49 \ln \left (x \right )^{2}-14 x \ln \left (x \right )-x^{2}+\ln \left (x \right )\right )}\) | \(31\) |
risch | \(2 x +\ln \left (x \right )-\frac {6}{\ln \left (-49 \ln \left (x \right )^{2}+\left (-14 x +1\right ) \ln \left (x \right )-x^{2}\right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 55 vs.
\(2 (25) = 50\).
time = 0.29, size = 55, normalized size = 2.20 \begin {gather*} \frac {2 \, {\left (x \log \left (-x^{2} - {\left (14 \, x - 1\right )} \log \left (x\right ) - 49 \, \log \left (x\right )^{2}\right ) - 3\right )}}{\log \left (-x^{2} - {\left (14 \, x - 1\right )} \log \left (x\right ) - 49 \, \log \left (x\right )^{2}\right )} + \log \left (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. 56 vs.
\(2 (25) = 50\).
time = 0.42, size = 56, normalized size = 2.24 \begin {gather*} \frac {{\left (2 \, x + \log \left (x\right )\right )} \log \left (-x^{2} - {\left (14 \, x - 1\right )} \log \left (x\right ) - 49 \, \log \left (x\right )^{2}\right ) - 6}{\log \left (-x^{2} - {\left (14 \, x - 1\right )} \log \left (x\right ) - 49 \, \log \left (x\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 27, normalized size = 1.08 \begin {gather*} 2 x + \log {\left (x \right )} - \frac {6}{\log {\left (- x^{2} + \left (1 - 14 x\right ) \log {\left (x \right )} - 49 \log {\left (x \right )}^{2} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 30, normalized size = 1.20 \begin {gather*} 2 \, x - \frac {6}{\log \left (-x^{2} - 14 \, x \log \left (x\right ) - 49 \, \log \left (x\right )^{2} + \log \left (x\right )\right )} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.27, size = 32, normalized size = 1.28 \begin {gather*} 2\,x+\ln \left (x\right )-\frac {6}{\ln \left (-49\,{\ln \left (x\right )}^2-\ln \left (x\right )\,\left (14\,x-1\right )-x^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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