Optimal. Leaf size=22 \[ 3+\frac {4+\frac {2}{x}+x}{e^4}+\log (x (13+5 x)) \]
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Rubi [A] time = 0.07, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 1593, 1620} \begin {gather*} \frac {x}{e^4}+\frac {2}{e^4 x}+\log (x)+\log (5 x+13) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1593
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-26-10 x+13 x^2+5 x^3+e^4 \left (13 x+10 x^2\right )}{13 x^2+5 x^3} \, dx}{e^4}\\ &=\frac {\int \frac {-26-10 x+13 x^2+5 x^3+e^4 \left (13 x+10 x^2\right )}{x^2 (13+5 x)} \, dx}{e^4}\\ &=\frac {\int \left (1-\frac {2}{x^2}+\frac {e^4}{x}+\frac {5 e^4}{13+5 x}\right ) \, dx}{e^4}\\ &=\frac {2}{e^4 x}+\frac {x}{e^4}+\log (x)+\log (13+5 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.23 \begin {gather*} \frac {\frac {2}{x}+x+e^4 \log (x)+e^4 \log (13+5 x)}{e^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 25, normalized size = 1.14 \begin {gather*} \frac {{\left (x e^{4} \log \left (5 \, x^{2} + 13 \, x\right ) + x^{2} + 2\right )} e^{\left (-4\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 26, normalized size = 1.18 \begin {gather*} {\left (e^{4} \log \left ({\left | 5 \, x + 13 \right |}\right ) + e^{4} \log \left ({\left | x \right |}\right ) + x + \frac {2}{x}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 23, normalized size = 1.05
method | result | size |
risch | \(x \,{\mathrm e}^{-4}+\frac {2 \,{\mathrm e}^{-4}}{x}+\ln \left (5 x^{2}+13 x \right )\) | \(23\) |
default | \({\mathrm e}^{-4} \left (x +{\mathrm e}^{4} \ln \relax (x )+\frac {2}{x}+{\mathrm e}^{4} \ln \left (13+5 x \right )\right )\) | \(27\) |
norman | \(\frac {x^{2} {\mathrm e}^{-4}+2 \,{\mathrm e}^{-4}}{x}+\ln \relax (x )+\ln \left (13+5 x \right )\) | \(29\) |
meijerg | \(-\frac {10 \,{\mathrm e}^{-4} \left (-\frac {13}{5 x}-\ln \relax (x )-\ln \relax (5)+\ln \left (13\right )+\ln \left (1+\frac {5 x}{13}\right )\right )}{13}+\frac {\left (10 \,{\mathrm e}^{4}+13\right ) {\mathrm e}^{-4} \ln \left (1+\frac {5 x}{13}\right )}{5}+\frac {\left (13 \,{\mathrm e}^{4}-10\right ) {\mathrm e}^{-4} \left (\ln \relax (x )+\ln \relax (5)-\ln \left (13\right )-\ln \left (1+\frac {5 x}{13}\right )\right )}{13}+\frac {13 \,{\mathrm e}^{-4} \left (\frac {5 x}{13}-\ln \left (1+\frac {5 x}{13}\right )\right )}{5}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 24, normalized size = 1.09 \begin {gather*} {\left (e^{4} \log \left (5 \, x + 13\right ) + e^{4} \log \relax (x) + x + \frac {2}{x}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 20, normalized size = 0.91 \begin {gather*} \ln \left (x\,\left (5\,x+13\right )\right )+x\,{\mathrm {e}}^{-4}+\frac {2\,{\mathrm {e}}^{-4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 20, normalized size = 0.91 \begin {gather*} \frac {x}{e^{4}} + \log {\left (5 x^{2} + 13 x \right )} + \frac {2}{x e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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