Optimal. Leaf size=18 \[ \log \left (30 \left (\frac {2}{5 (4-x)}+7 x\right )\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps
used = 3, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2099, 642}
\begin {gather*} \log \left (-35 x^2+140 x+2\right )-\log (4-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{4-x}+\frac {70 (-2+x)}{-2-140 x+35 x^2}\right ) \, dx\\ &=-\log (4-x)+70 \int \frac {-2+x}{-2-140 x+35 x^2} \, dx\\ &=-\log (4-x)+\log \left (2+140 x-35 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 20, normalized size = 1.11 \begin {gather*} -\log (4-x)+\log \left (2+140 x-35 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 19, normalized size = 1.06
method | result | size |
default | \(\ln \left (35 x^{2}-140 x -2\right )-\ln \left (x -4\right )\) | \(19\) |
norman | \(\ln \left (35 x^{2}-140 x -2\right )-\ln \left (x -4\right )\) | \(19\) |
risch | \(\ln \left (35 x^{2}-140 x -2\right )-\ln \left (x -4\right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.48, size = 18, normalized size = 1.00 \begin {gather*} \log \left (35 \, x^{2} - 140 \, x - 2\right ) - \log \left (x - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 18, normalized size = 1.00 \begin {gather*} \log \left (35 \, x^{2} - 140 \, x - 2\right ) - \log \left (x - 4\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 = 0.83 \begin {gather*} - \log {\left (x - 4 \right )} + \log {\left (35 x^{2} - 140 x - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 20, normalized size = 1.11 \begin {gather*} \log \left ({\left | 35 \, x^{2} - 140 \, x - 2 \right |}\right ) - \log \left ({\left | x - 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 16, normalized size = 0.89 \begin {gather*} \ln \left (x^2-4\,x-\frac {2}{35}\right )-\ln \left (x-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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