Optimal. Leaf size=17 \[ \frac{x^2}{2}-x+2 \log (x+1) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0083317, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {697} \[ \frac{x^2}{2}-x+2 \log (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 697
Rubi steps
\begin{align*} \int \frac{1+x^2}{1+x} \, dx &=\int \left (-1+x+\frac{2}{1+x}\right ) \, dx\\ &=-x+\frac{x^2}{2}+2 \log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0027629, size = 18, normalized size = 1.06 \[ \frac{1}{2} \left (x^2-2 x+4 \log (x+1)-3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 16, normalized size = 0.9 \begin{align*} -x+{\frac{{x}^{2}}{2}}+2\,\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09184, size = 20, normalized size = 1.18 \begin{align*} \frac{1}{2} \, x^{2} - x + 2 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.20878, size = 38, normalized size = 2.24 \begin{align*} \frac{1}{2} \, x^{2} - x + 2 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.069357, size = 12, normalized size = 0.71 \begin{align*} \frac{x^{2}}{2} - x + 2 \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.09614, size = 22, normalized size = 1.29 \begin{align*} \frac{1}{2} \, x^{2} - x + 2 \, \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]