Optimal. Leaf size=21 \[ -\frac {3}{2 (1-x)^2}+\frac {2}{1-x} \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2099}
\begin {gather*} \frac {2}{1-x}-\frac {3}{2 (1-x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2099
Rubi steps
\begin {align*} \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx &=\int \left (\frac {3}{(-1+x)^3}+\frac {2}{(-1+x)^2}\right ) \, dx\\ &=-\frac {3}{2 (1-x)^2}+\frac {2}{1-x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.67 \begin {gather*} \frac {1-4 x}{2 (-1+x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 16, normalized size = 0.76
method | result | size |
norman | \(\frac {-2 x +\frac {1}{2}}{\left (-1+x \right )^{2}}\) | \(12\) |
default | \(-\frac {2}{-1+x}-\frac {3}{2 \left (-1+x \right )^{2}}\) | \(16\) |
risch | \(\frac {-2 x +\frac {1}{2}}{x^{2}-2 x +1}\) | \(17\) |
gosper | \(-\frac {4 x -1}{2 \left (x^{2}-2 x +1\right )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 0.81 \begin {gather*} -\frac {4 \, x - 1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 17, normalized size = 0.81 \begin {gather*} -\frac {4 \, x - 1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.67 \begin {gather*} \frac {1 - 4 x}{2 x^{2} - 4 x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.93, size = 12, normalized size = 0.57 \begin {gather*} -\frac {4 \, x - 1}{2 \, {\left (x - 1\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.09, size = 12, normalized size = 0.57 \begin {gather*} -\frac {4\,x-1}{2\,{\left (x-1\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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