Optimal. Leaf size=20 \[ \left (10+\frac {1}{4-x+5 (3+x)}-\log (3)\right )^2 \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 1.15, number of steps used = 2, number of rules used = 1, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {2074} \begin {gather*} \frac {1}{(4 x+19)^2}+\frac {2 (10-\log (3))}{4 x+19} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {8}{(19+4 x)^3}+\frac {8 (-10+\log (3))}{(19+4 x)^2}\right ) \, dx\\ &=\frac {1}{(19+4 x)^2}+\frac {2 (10-\log (3))}{19+4 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.05 \begin {gather*} \frac {381-8 x (-10+\log (3))-38 \log (3)}{(19+4 x)^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 28, normalized size = 1.40 \begin {gather*} -\frac {2 \, {\left (4 \, x + 19\right )} \log \relax (3) - 80 \, x - 381}{16 \, x^{2} + 152 \, x + 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 23, normalized size = 1.15 \begin {gather*} -\frac {8 \, x \log \relax (3) - 80 \, x + 38 \, \log \relax (3) - 381}{{\left (4 \, x + 19\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 1.15
method | result | size |
norman | \(\frac {\left (80-8 \ln \relax (3)\right ) x +381-38 \ln \relax (3)}{\left (4 x +19\right )^{2}}\) | \(23\) |
default | \(-\frac {8 \left (\frac {\ln \relax (3)}{4}-\frac {5}{2}\right )}{4 x +19}+\frac {1}{\left (4 x +19\right )^{2}}\) | \(24\) |
risch | \(\frac {\left (-\frac {\ln \relax (3)}{2}+5\right ) x +\frac {381}{16}-\frac {19 \ln \relax (3)}{8}}{x^{2}+\frac {19}{2} x +\frac {361}{16}}\) | \(26\) |
gosper | \(-\frac {8 x \ln \relax (3)+38 \ln \relax (3)-80 x -381}{16 x^{2}+152 x +361}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 27, normalized size = 1.35 \begin {gather*} -\frac {8 \, x {\left (\log \relax (3) - 10\right )} + 38 \, \log \relax (3) - 381}{16 \, x^{2} + 152 \, x + 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 23, normalized size = 1.15 \begin {gather*} \frac {1}{{\left (4\,x+19\right )}^2}-\frac {2\,\ln \relax (3)-20}{4\,x+19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.19, size = 26, normalized size = 1.30 \begin {gather*} - \frac {x \left (-80 + 8 \log {\relax (3 )}\right ) - 381 + 38 \log {\relax (3 )}}{16 x^{2} + 152 x + 361} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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