Optimal. Leaf size=19 \[ -33 \left (2 x-\frac {3}{\log \left (-2-x+x^2\right )}\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps
used = 3, number of rules used = 2, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6860, 6818}
\begin {gather*} \frac {99}{\log \left (x^2-x-2\right )}-66 x \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6860
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-66-\frac {99 (-1+2 x)}{(-2+x) (1+x) \log ^2\left (-2-x+x^2\right )}\right ) \, dx\\ &=-66 x-99 \int \frac {-1+2 x}{(-2+x) (1+x) \log ^2\left (-2-x+x^2\right )} \, dx\\ &=-66 x+\frac {99}{\log \left (-2-x+x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 19, normalized size = 1.00 \begin {gather*} -33 \left (2 x-\frac {3}{\log \left (-2-x+x^2\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.98, size = 18, normalized size = 0.95
method | result | size |
default | \(-66 x +\frac {99}{\ln \left (x^{2}-x -2\right )}\) | \(18\) |
risch | \(-66 x +\frac {99}{\ln \left (x^{2}-x -2\right )}\) | \(18\) |
norman | \(\frac {99-66 \ln \left (x^{2}-x -2\right ) x}{\ln \left (x^{2}-x -2\right )}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 29, normalized size = 1.53 \begin {gather*} -\frac {33 \, {\left (2 \, x \log \left (x + 1\right ) + 2 \, x \log \left (x - 2\right ) - 3\right )}}{\log \left (x + 1\right ) + \log \left (x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 27, normalized size = 1.42 \begin {gather*} -\frac {33 \, {\left (2 \, x \log \left (x^{2} - x - 2\right ) - 3\right )}}{\log \left (x^{2} - x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 12, normalized size = 0.63 \begin {gather*} - 66 x + \frac {99}{\log {\left (x^{2} - x - 2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 17, normalized size = 0.89 \begin {gather*} -66 \, x + \frac {99}{\log \left (x^{2} - x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.33, size = 17, normalized size = 0.89 \begin {gather*} \frac {99}{\ln \left (x^2-x-2\right )}-66\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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