Optimal. Leaf size=21 \[ \frac{2}{1-x}-\frac{3}{2 (1-x)^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0192289, antiderivative size = 21, normalized size of antiderivative = 1., 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.
[In]
[Out]
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*}
Mathematica [A] time = 0.0033034, size = 14, normalized size = 0.67 \[ \frac{1-4 x}{2 (x-1)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 16, normalized size = 0.8 \begin{align*} -2\, \left ( x-1 \right ) ^{-1}-{\frac{3}{2\, \left ( x-1 \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.998447, size = 23, normalized size = 1.1 \begin{align*} -\frac{4 \, x - 1}{2 \,{\left (x^{2} - 2 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.45897, size = 43, normalized size = 2.05 \begin{align*} -\frac{4 \, x - 1}{2 \,{\left (x^{2} - 2 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.084257, size = 15, normalized size = 0.71 \begin{align*} - \frac{4 x - 1}{2 x^{2} - 4 x + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13127, size = 16, normalized size = 0.76 \begin{align*} -\frac{4 \, x - 1}{2 \,{\left (x - 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]