Optimal. Leaf size=21 \[ \frac {2}{1-x}-\frac {3}{2 (1-x)^2} \]
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Rubi [A] time = 0.02, 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 = {2074} \[ \frac {2}{1-x}-\frac {3}{2 (1-x)^2} \]
Antiderivative was successfully verified.
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Rule 2074
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 \[ \frac {1-4 x}{2 (x-1)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 17, normalized size = 0.81 \[ -\frac {4 \, x - 1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 12, normalized size = 0.57 \[ -\frac {4 \, x - 1}{2 \, {\left (x - 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.76 \[ -\frac {3}{2 \left (x -1\right )^{2}}-\frac {2}{x -1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 17, normalized size = 0.81 \[ -\frac {4 \, x - 1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \]
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 \[ -\frac {4\,x-1}{2\,{\left (x-1\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.67 \[ \frac {1 - 4 x}{2 x^{2} - 4 x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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