Optimal. Leaf size=14 \[ x^2+\log (\log (-2+x+12 (3+x))) \]
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Rubi [A] time = 0.11, antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 5, number of rules used = 4, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {6688, 2390, 2302, 29} \begin {gather*} x^2+\log (\log (13 x+34)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2302
Rule 2390
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \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+\operatorname {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,34+13 x\right )\\ &=x^2+\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (34+13 x)\right )\\ &=x^2+\log (\log (34+13 x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 11, normalized size = 0.79 \begin {gather*} x^2+\log (\log (34+13 x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 11, normalized size = 0.79 \begin {gather*} x^{2} + \log \left (\log \left (13 \, x + 34\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 11, normalized size = 0.79 \begin {gather*} x^{2} + \log \left (\log \left (13 \, x + 34\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 12, normalized size = 0.86
method | result | size |
norman | \(x^{2}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(12\) |
risch | \(x^{2}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(12\) |
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 | \(\frac {\left (13 x +34\right )^{2}}{169}-\frac {68 x}{13}-\frac {2312}{169}+\ln \left (\ln \left (13 x +34\right )\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 11, normalized size = 0.79 \begin {gather*} x^{2} + \log \left (\log \left (13 \, x + 34\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.81, size = 11, normalized size = 0.79 \begin {gather*} \ln \left (\ln \left (13\,x+34\right )\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 0.71 \begin {gather*} x^{2} + \log {\left (\log {\left (13 x + 34 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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