Optimal. Leaf size=35 \[ \frac {x^2}{2}-2 x+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (x+2)+20 \log (x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2074} \[ \frac {x^2}{2}-2 x+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (x+2)+20 \log (x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2074
Rubi steps
\begin {align*} \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx &=\int \left (-2+\frac {13}{3 (-4+x)}+x-\frac {22}{3 (2+x)}+\frac {20}{3+x}\right ) \, dx\\ &=-2 x+\frac {x^2}{2}+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (2+x)+20 \log (3+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 35, normalized size = 1.00 \[ \frac {x^2}{2}-2 x+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (x+2)+20 \log (x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.75, size = 27, normalized size = 0.77 \[ \frac {1}{2} \, x^{2} - 2 \, x + 20 \, \log \left (x + 3\right ) - \frac {22}{3} \, \log \left (x + 2\right ) + \frac {13}{3} \, \log \left (x - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.32, size = 30, normalized size = 0.86 \[ \frac {1}{2} \, x^{2} - 2 \, x + 20 \, \log \left ({\left | x + 3 \right |}\right ) - \frac {22}{3} \, \log \left ({\left | x + 2 \right |}\right ) + \frac {13}{3} \, \log \left ({\left | x - 4 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 28, normalized size = 0.80 \[ \frac {x^{2}}{2}-2 x -\frac {22 \ln \left (x +2\right )}{3}+20 \ln \left (x +3\right )+\frac {13 \ln \left (x -4\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.12, size = 27, normalized size = 0.77 \[ \frac {1}{2} \, x^{2} - 2 \, x + 20 \, \log \left (x + 3\right ) - \frac {22}{3} \, \log \left (x + 2\right ) + \frac {13}{3} \, \log \left (x - 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 27, normalized size = 0.77 \[ 20\,\ln \left (x+3\right )-\frac {22\,\ln \left (x+2\right )}{3}-2\,x+\frac {13\,\ln \left (x-4\right )}{3}+\frac {x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 31, normalized size = 0.89 \[ \frac {x^{2}}{2} - 2 x + \frac {13 \log {\left (x - 4 \right )}}{3} - \frac {22 \log {\left (x + 2 \right )}}{3} + 20 \log {\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________