Optimal. Leaf size=20 \[ -x+\frac {10-4 \log ^4(2)}{2-x} \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps
used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {27, 697}
\begin {gather*} \frac {2 \left (5-2 \log ^4(2)\right )}{2-x}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 697
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6+4 x-x^2-4 \log ^4(2)}{(-2+x)^2} \, dx\\ &=\int \left (-1-\frac {2 \left (-5+2 \log ^4(2)\right )}{(-2+x)^2}\right ) \, dx\\ &=-x+\frac {2 \left (5-2 \log ^4(2)\right )}{2-x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 0.95 \begin {gather*} -x+\frac {2 \left (-5+2 \log ^4(2)\right )}{-2+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.30, size = 20, normalized size = 1.00
method | result | size |
gosper | \(\frac {4 \ln \left (2\right )^{4}-x^{2}-6}{x -2}\) | \(20\) |
default | \(-x -\frac {10-4 \ln \left (2\right )^{4}}{x -2}\) | \(20\) |
risch | \(-x +\frac {4 \ln \left (2\right )^{4}}{x -2}-\frac {10}{x -2}\) | \(23\) |
meijerg | \(\frac {7 x}{2 \left (1-\frac {x}{2}\right )}-\frac {\ln \left (2\right )^{4} x}{1-\frac {x}{2}}-\frac {x \left (-\frac {3 x}{2}+6\right )}{3 \left (1-\frac {x}{2}\right )}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 0.95 \begin {gather*} -x + \frac {2 \, {\left (2 \, \log \left (2\right )^{4} - 5\right )}}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 22, normalized size = 1.10 \begin {gather*} \frac {4 \, \log \left (2\right )^{4} - x^{2} + 2 \, x - 10}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.70 \begin {gather*} - x - \frac {10 - 4 \log {\left (2 \right )}^{4}}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 19, normalized size = 0.95 \begin {gather*} -x + \frac {2 \, {\left (2 \, \log \left (2\right )^{4} - 5\right )}}{x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.22, size = 18, normalized size = 0.90 \begin {gather*} \frac {4\,{\ln \left (2\right )}^4-10}{x-2}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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