Optimal. Leaf size=23 \[ -4-\frac {x}{2 (256-x)}-\log (5)+3 e \log (x) \]
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Rubi [A]
time = 0.03, antiderivative size = 15, normalized size of antiderivative = 0.65, number of steps
used = 4, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {1608, 27, 1834}
\begin {gather*} 3 e \log (x)-\frac {128}{256-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1608
Rule 1834
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-128 x+e \left (196608-1536 x+3 x^2\right )}{x \left (65536-512 x+x^2\right )} \, dx\\ &=\int \frac {-128 x+e \left (196608-1536 x+3 x^2\right )}{(-256+x)^2 x} \, dx\\ &=\int \left (-\frac {128}{(-256+x)^2}+\frac {3 e}{x}\right ) \, dx\\ &=-\frac {128}{256-x}+3 e \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 0.57 \begin {gather*} \frac {128}{-256+x}+3 e \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 15, normalized size = 0.65
method | result | size |
default | \(\frac {128}{x -256}+3 \,{\mathrm e} \ln \left (x \right )\) | \(15\) |
norman | \(\frac {128}{x -256}+3 \,{\mathrm e} \ln \left (x \right )\) | \(15\) |
risch | \(\frac {128}{x -256}+3 \,{\mathrm e} \ln \left (-x \right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 14, normalized size = 0.61 \begin {gather*} 3 \, e \log \left (x\right ) + \frac {128}{x - 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 17, normalized size = 0.74 \begin {gather*} \frac {3 \, {\left (x - 256\right )} e \log \left (x\right ) + 128}{x - 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 12, normalized size = 0.52 \begin {gather*} 3 e \log {\left (x \right )} + \frac {128}{x - 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 15, normalized size = 0.65 \begin {gather*} 3 \, e \log \left ({\left | x \right |}\right ) + \frac {128}{x - 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 14, normalized size = 0.61 \begin {gather*} \frac {128}{x-256}+3\,\mathrm {e}\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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