Optimal. Leaf size=23 \[ \frac {13}{4}-x+\frac {5}{\log \left (-4-\frac {3}{x}+x+x^2\right )} \]
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Rubi [A]
time = 0.16, antiderivative size = 20, normalized size of antiderivative = 0.87, number of steps
used = 3, number of rules used = 2, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6820, 6818}
\begin {gather*} \frac {5}{\log \left (x^2+x-\frac {3}{x}-4\right )}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {5 \left (3+x^2+2 x^3\right )}{x \left (-3-4 x+x^2+x^3\right ) \log ^2\left (-4-\frac {3}{x}+x+x^2\right )}\right ) \, dx\\ &=-x-5 \int \frac {3+x^2+2 x^3}{x \left (-3-4 x+x^2+x^3\right ) \log ^2\left (-4-\frac {3}{x}+x+x^2\right )} \, dx\\ &=-x+\frac {5}{\log \left (-4-\frac {3}{x}+x+x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 20, normalized size = 0.87 \begin {gather*} -x+\frac {5}{\log \left (-4-\frac {3}{x}+x+x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 25, normalized size = 1.09
method | result | size |
default | \(-x +\frac {5}{\ln \left (\frac {x^{3}+x^{2}-4 x -3}{x}\right )}\) | \(25\) |
risch | \(-x +\frac {5}{\ln \left (\frac {x^{3}+x^{2}-4 x -3}{x}\right )}\) | \(25\) |
norman | \(\frac {5-x \ln \left (\frac {x^{3}+x^{2}-4 x -3}{x}\right )}{\ln \left (\frac {x^{3}+x^{2}-4 x -3}{x}\right )}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 42, normalized size = 1.83 \begin {gather*} -\frac {x \log \left (x^{3} + x^{2} - 4 \, x - 3\right ) - x \log \left (x\right ) - 5}{\log \left (x^{3} + x^{2} - 4 \, x - 3\right ) - \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 40, normalized size = 1.74 \begin {gather*} -\frac {x \log \left (\frac {x^{3} + x^{2} - 4 \, x - 3}{x}\right ) - 5}{\log \left (\frac {x^{3} + x^{2} - 4 \, x - 3}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.74 \begin {gather*} - x + \frac {5}{\log {\left (\frac {x^{3} + x^{2} - 4 x - 3}{x} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.52, size = 24, normalized size = 1.04 \begin {gather*} -x + \frac {5}{\log \left (\frac {x^{3} + x^{2} - 4 \, x - 3}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.55, size = 29, normalized size = 1.26 \begin {gather*} \frac {5}{\ln \left (-\frac {-x^3-x^2+4\,x+3}{x}\right )}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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