Integrand size = 34, antiderivative size = 14 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^2+\log (\log (-2+x+12 (3+x))) \]
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Time = 0.07 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 5, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {6820, 2437, 2339, 29} \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^2+\log (\log (13 x+34)) \]
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Rule 29
Rule 2339
Rule 2437
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \left (2 x+\frac {13}{(34+13 x) \log (34+13 x)}\right ) \, dx \\ & = x^2+13 \int \frac {1}{(34+13 x) \log (34+13 x)} \, dx \\ & = x^2+\text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,34+13 x\right ) \\ & = x^2+\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (34+13 x)\right ) \\ & = x^2+\log (\log (34+13 x)) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^2+\log (\log (34+13 x)) \]
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Time = 0.38 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86
method | result | size |
norman | \(x^{2}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(12\) |
risch | \(x^{2}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(12\) |
parts | \(x^{2}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(12\) |
parallelrisch | \(-\frac {1156}{169}+x^{2}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(13\) |
derivativedivides | \(\frac {\left (13 x +34\right )^{2}}{169}-\frac {68 x}{13}-\frac {2312}{169}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(22\) |
default | \(\frac {\left (13 x +34\right )^{2}}{169}-\frac {68 x}{13}-\frac {2312}{169}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(22\) |
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Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^{2} + \log \left (\log \left (13 \, x + 34\right )\right ) \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^{2} + \log {\left (\log {\left (13 x + 34 \right )} \right )} \]
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Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^{2} + \log \left (\log \left (13 \, x + 34\right )\right ) \]
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Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=x^{2} + \log \left (\log \left (13 \, x + 34\right )\right ) \]
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Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {13+\left (68 x+26 x^2\right ) \log (34+13 x)}{(34+13 x) \log (34+13 x)} \, dx=\ln \left (\ln \left (13\,x+34\right )\right )+x^2 \]
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