Optimal. Leaf size=17 \[ \frac {4-x}{1+x}-4 x \log (2) \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.76, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {27, 1850} \begin {gather*} \frac {5}{x+1}-4 x \log (2) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-5+\left (-4-8 x-4 x^2\right ) \log (2)}{(1+x)^2} \, dx\\ &=\int \left (-\frac {5}{(1+x)^2}-4 \log (2)\right ) \, dx\\ &=\frac {5}{1+x}-4 x \log (2)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 21, normalized size = 1.24 \begin {gather*} -\frac {-5+\log (16)+x^2 \log (16)+x \log (256)}{1+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 18, normalized size = 1.06 \begin {gather*} -\frac {4 \, {\left (x^{2} + x\right )} \log \relax (2) - 5}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.76 \begin {gather*} -4 \, x \log \relax (2) + \frac {5}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 14, normalized size = 0.82
method | result | size |
default | \(-4 x \ln \relax (2)+\frac {5}{x +1}\) | \(14\) |
risch | \(-4 x \ln \relax (2)+\frac {5}{x +1}\) | \(14\) |
norman | \(\frac {-4 x^{2} \ln \relax (2)+5+4 \ln \relax (2)}{x +1}\) | \(20\) |
gosper | \(-\frac {4 x^{2} \ln \relax (2)-5-4 \ln \relax (2)}{x +1}\) | \(21\) |
meijerg | \(-\frac {5 x}{x +1}-4 \ln \relax (2) \left (\frac {x \left (6+3 x \right )}{3 x +3}-2 \ln \left (x +1\right )\right )-8 \ln \relax (2) \left (-\frac {x}{x +1}+\ln \left (x +1\right )\right )-\frac {4 \ln \relax (2) x}{x +1}\) | \(61\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.76 \begin {gather*} -4 \, x \log \relax (2) + \frac {5}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 13, normalized size = 0.76 \begin {gather*} \frac {5}{x+1}-4\,x\,\ln \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.59 \begin {gather*} - 4 x \log {\relax (2 )} + \frac {5}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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