Optimal. Leaf size=15 \[ \frac {1}{1-x}-\frac {2}{(x+1)^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {1620} \[ \frac {1}{1-x}-\frac {2}{(x+1)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1620
Rubi steps
\begin {align*} \int \frac {5-5 x+7 x^2+x^3}{(-1+x)^2 (1+x)^3} \, dx &=\int \left (\frac {1}{(-1+x)^2}+\frac {4}{(1+x)^3}\right ) \, dx\\ &=\frac {1}{1-x}-\frac {2}{(1+x)^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \[ -\frac {2}{(x+1)^2}-\frac {1}{x-1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.88, size = 23, normalized size = 1.53 \[ -\frac {x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.26, size = 30, normalized size = 2.00 \[ -\frac {1}{x - 1} + \frac {\frac {4}{x - 1} + 1}{2 \, {\left (\frac {2}{x - 1} + 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 16, normalized size = 1.07 \[ -\frac {2}{\left (x +1\right )^{2}}-\frac {1}{x -1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.27, size = 23, normalized size = 1.53 \[ -\frac {x^{2} + 4 \, x - 1}{x^{3} + x^{2} - x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.09, size = 15, normalized size = 1.00 \[ -\frac {1}{x-1}-\frac {2}{{\left (x+1\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 17, normalized size = 1.13 \[ \frac {- x^{2} - 4 x + 1}{x^{3} + x^{2} - x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________