Optimal. Leaf size=28 \[ \frac {4}{3 \left (-5+5 x^2\right )}+\log \left (\frac {\left (x-x^2\right )^2}{x^2}\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 22, normalized size of antiderivative = 0.79, number of steps used = 4, number of rules used = 4, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {28, 1814, 627, 31} \begin {gather*} 2 \log (1-x)-\frac {4}{15 \left (1-x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 31
Rule 627
Rule 1814
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=15 \int \frac {-30-38 x+30 x^2+30 x^3}{\left (-15+15 x^2\right )^2} \, dx\\ &=-\frac {4}{15 \left (1-x^2\right )}+\frac {1}{2} \int \frac {60+60 x}{-15+15 x^2} \, dx\\ &=-\frac {4}{15 \left (1-x^2\right )}+\frac {1}{2} \int \frac {1}{-\frac {1}{4}+\frac {x}{4}} \, dx\\ &=-\frac {4}{15 \left (1-x^2\right )}+2 \log (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.79 \begin {gather*} \frac {2}{15} \left (\frac {2}{-1+x^2}+15 \log (1-x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 22, normalized size = 0.79 \begin {gather*} \frac {2 \, {\left (15 \, {\left (x^{2} - 1\right )} \log \left (x - 1\right ) + 2\right )}}{15 \, {\left (x^{2} - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 20, normalized size = 0.71 \begin {gather*} \frac {4}{15 \, {\left (x + 1\right )} {\left (x - 1\right )}} + 2 \, \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.61
method | result | size |
norman | \(\frac {4}{15 \left (x^{2}-1\right )}+2 \ln \left (x -1\right )\) | \(17\) |
risch | \(\frac {4}{15 \left (x^{2}-1\right )}+2 \ln \left (x -1\right )\) | \(17\) |
default | \(-\frac {2}{15 \left (x +1\right )}+\frac {2}{15 \left (x -1\right )}+2 \ln \left (x -1\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 16, normalized size = 0.57 \begin {gather*} \frac {4}{15 \, {\left (x^{2} - 1\right )}} + 2 \, \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 18, normalized size = 0.64 \begin {gather*} 2\,\ln \left (x-1\right )+\frac {4}{15\,\left (x^2-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.50 \begin {gather*} 2 \log {\left (x - 1 \right )} + \frac {4}{15 x^{2} - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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