Optimal. Leaf size=23 \[ 2 x+\frac {x^2}{2}+9 \log (3-x)+\log (1+x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 4, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {1607, 1642,
646, 31} \begin {gather*} \frac {x^2}{2}+2 x+9 \log (3-x)+\log (x+1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 646
Rule 1607
Rule 1642
Rubi steps
\begin {align*} \int \frac {3 x+x^3}{-3-2 x+x^2} \, dx &=\int \frac {x \left (3+x^2\right )}{-3-2 x+x^2} \, dx\\ &=\int \left (2+x+\frac {2 (3+5 x)}{-3-2 x+x^2}\right ) \, dx\\ &=2 x+\frac {x^2}{2}+2 \int \frac {3+5 x}{-3-2 x+x^2} \, dx\\ &=2 x+\frac {x^2}{2}+9 \int \frac {1}{-3+x} \, dx+\int \frac {1}{1+x} \, dx\\ &=2 x+\frac {x^2}{2}+9 \log (3-x)+\log (1+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 23, normalized size = 1.00 \begin {gather*} 2 x+\frac {x^2}{2}+9 \log (3-x)+\log (1+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 20, normalized size = 0.87
method | result | size |
default | \(2 x +\frac {x^{2}}{2}+9 \ln \left (-3+x \right )+\ln \left (1+x \right )\) | \(20\) |
norman | \(2 x +\frac {x^{2}}{2}+9 \ln \left (-3+x \right )+\ln \left (1+x \right )\) | \(20\) |
risch | \(2 x +\frac {x^{2}}{2}+9 \ln \left (-3+x \right )+\ln \left (1+x \right )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.96, size = 19, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, x^{2} + 2 \, x + \log \left (x + 1\right ) + 9 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.82, size = 19, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, x^{2} + 2 \, x + \log \left (x + 1\right ) + 9 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 19, normalized size = 0.83 \begin {gather*} \frac {x^{2}}{2} + 2 x + 9 \log {\left (x - 3 \right )} + \log {\left (x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.44, size = 21, normalized size = 0.91 \begin {gather*} \frac {1}{2} \, x^{2} + 2 \, x + \log \left ({\left | x + 1 \right |}\right ) + 9 \, \log \left ({\left | x - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 19, normalized size = 0.83 \begin {gather*} 2\,x+\ln \left (x+1\right )+9\,\ln \left (x-3\right )+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________