Optimal. Leaf size=24 \[ \frac{1}{x+1}+\frac{3}{2} \log (1-x)-\frac{1}{2} \log (x+1) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0143797, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {893} \[ \frac{1}{x+1}+\frac{3}{2} \log (1-x)-\frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 893
Rubi steps
\begin{align*} \int \frac{3+2 x+x^2}{(-1+x) (1+x)^2} \, dx &=\int \left (\frac{3}{2 (-1+x)}-\frac{1}{(1+x)^2}-\frac{1}{2 (1+x)}\right ) \, dx\\ &=\frac{1}{1+x}+\frac{3}{2} \log (1-x)-\frac{1}{2} \log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0083749, size = 22, normalized size = 0.92 \[ \frac{1}{x+1}+\frac{3}{2} \log (x-1)-\frac{1}{2} \log (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 19, normalized size = 0.8 \begin{align*} \left ( 1+x \right ) ^{-1}-{\frac{\ln \left ( 1+x \right ) }{2}}+{\frac{3\,\ln \left ( -1+x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.947586, size = 24, normalized size = 1. \begin{align*} \frac{1}{x + 1} - \frac{1}{2} \, \log \left (x + 1\right ) + \frac{3}{2} \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.666378, size = 84, normalized size = 3.5 \begin{align*} -\frac{{\left (x + 1\right )} \log \left (x + 1\right ) - 3 \,{\left (x + 1\right )} \log \left (x - 1\right ) - 2}{2 \,{\left (x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.104982, size = 19, normalized size = 0.79 \begin{align*} \frac{3 \log{\left (x - 1 \right )}}{2} - \frac{\log{\left (x + 1 \right )}}{2} + \frac{1}{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.09003, size = 32, normalized size = 1.33 \begin{align*} \frac{1}{x + 1} + \log \left ({\left | x + 1 \right |}\right ) + \frac{3}{2} \, \log \left ({\left | -\frac{2}{x + 1} + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]