Optimal. Leaf size=20 \[ -e^{25}+4 \left (-17+\log \left (e^x \left (5+\frac {1}{x}\right )\right )\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1607, 907}
\begin {gather*} 4 x-4 \log (x)+4 \log (5 x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 907
Rule 1607
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4+4 x+20 x^2}{x (1+5 x)} \, dx\\ &=\int \left (4-\frac {4}{x}+\frac {20}{1+5 x}\right ) \, dx\\ &=4 x-4 \log (x)+4 \log (1+5 x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.70 \begin {gather*} 4 (x-\log (x)+\log (1+5 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.83, size = 17, normalized size = 0.85
method | result | size |
default | \(4 x -4 \ln \left (x \right )+4 \ln \left (1+5 x \right )\) | \(17\) |
norman | \(4 x -4 \ln \left (x \right )+4 \ln \left (1+5 x \right )\) | \(17\) |
risch | \(4 x -4 \ln \left (x \right )+4 \ln \left (1+5 x \right )\) | \(17\) |
meijerg | \(4 x +4 \ln \left (1+5 x \right )-4 \ln \left (5\right )-4 \ln \left (x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 16, normalized size = 0.80 \begin {gather*} 4 \, x + 4 \, \log \left (5 \, x + 1\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 16, normalized size = 0.80 \begin {gather*} 4 \, x + 4 \, \log \left (5 \, x + 1\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.75 \begin {gather*} 4 x - 4 \log {\left (x \right )} + 4 \log {\left (x + \frac {1}{5} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 18, normalized size = 0.90 \begin {gather*} 4 \, x + 4 \, \log \left ({\left | 5 \, x + 1 \right |}\right ) - 4 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 12, normalized size = 0.60 \begin {gather*} 4\,x+8\,\mathrm {atanh}\left (10\,x+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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